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1900 - 1999

1900

19002± 3 are primes.

19002 = 3610000, and 36 = 62, 10000 = 1002.

19002 = (1)(2 + 3)(4 + 5 + 6 + ... + 28)(29 + 30 + 31 + ... + 66).

Page of Squares : First Upload March 5, 2007 ; Last Revised January 16, 2014
by Yoshio Mimura, Kobe, Japan

1902

19022± 5 are primes.

Page of Squares : First Upload January 16, 2014 ; Last Revised January 16, 2014
by Yoshio Mimura, Kobe, Japan

1903

19032 = 3621409, a square with different digits.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1904

19045 = 25022731752833024 :
252 + 02 + 222 + 72 + 32 + 12 + 72 + 52 + 22 + 82 + 32 + 32 + 02 + 242 = 1904.

Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

1906

19062 = 3632836, and 3 * 632 - 8 + 3 * 6 = 1906.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1907

19072 = 3636649, and 3 * 636 - 6 - 4 + 9 = 1907.

19172 = 1! + 1! + 1! + 3! + 6! + 7! + 8! + 10! = 1! + 2! + 3! + 6! + 7! + 8! + 10!.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 7, 2007
by Yoshio Mimura, Kobe, Japan

1909

19092 = 3644281 appears in the decimal expressions of e:
  e = 2.71828•••3644281••• (from the 1887th digit)
  (3644281 is the second 7-digit square in the expression of e.)

Page of Squares : First Upload November 4, 2008 ; Last Revised November 4, 2008
by Yoshio Mimura, Kobe, Japan

1910

The sum of the divisors of 19102 is a square, 28212.

Page of Squares : First Upload November 1, 2011 ; Last Revised November 1, 2011
by Yoshio Mimura, Kobe, Japan

1911

19112 = (62 + 3)(3062 + 3).

Page of Squares : First Upload November 1, 2011 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

1912

19122± 3 are primes.

19122 = 233 + 813 + 1463 = 923 + 1023 + 1223 = 24 + 224 + 344 + 384.

Page of Squares : First Upload July 14, 2008 ; Last Revised January 16, 2014
by Yoshio Mimura, Kobe, Japan

1913

19132 = 3659569, 3 * 659 + 5 - 69 = 1913.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1914

19142 = 3663396, a square with jst 3 kinds of digits.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1916

19162 = 3671056 appears in the decimal expressions of e:
  e = 2.71828•••3671056••• (from the 50873rd digit)

Page of Squares : First Upload November 4, 2008 ; Last Revised November 4, 2008
by Yoshio Mimura, Kobe, Japan

1917

19172 = 363 + 363 + 1533 = 363 + 1143 + 1293 = 543 + 813 + 1443.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1918

19182 = 3678724 appears in the decimal expressions of e:
  e = 2.71828•••3678724••• (from the 54950th digit)

Page of Squares : First Upload November 4, 2008 ; Last Revised November 4, 2008
by Yoshio Mimura, Kobe, Japan

1920

A cubic polynomial :
(X + 19202)(X + 27372)(X + 36002) = X3 + 49132X2 + 131330402X + 189181440002.

19202 = 3686400, and 36 * 8 / 6 * 40 + 0 = 1920.

19202 = 6! + 6! + 6! + 7! + 7! + 7! + 8! + 10!.

19202 = (32 - 1)(72 - 1)(92 - 1)(112 - 1) = (72 - 1)(92 - 1)(312 - 1).

19202 = 103 + 473 + 1533 = 403 + 483 + 1523.

522 + 1920 = 682, 522 - 1920 = 282.

Page of Squares : First Upload March 5, 2007 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

1921

19212 = 3690241, a square with differential digits.

19212 = 254 + 304 + 304 + 364.

Page of Squares : First Upload March 5, 2007 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1922

19222 = 114 + 194 + 194 + 434 = 314 + 314 + 314 + 314.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1924

19242± 3 are primes.

19242 = 244 + 304 + 404.

Page of Squares : First Upload July 14, 2008 ; Last Revised January 16, 2014
by Yoshio Mimura, Kobe, Japan

1925

1925 = (12 + 22 + 32 + ... + 12872) / (12 + 22 + 32 + ... + 1032).

19252 = (1)(2 + 3 + 4 + ... + 12)(13 + 14 + 15 + ... + 22)(23 + 24 + 25 + ... + 32),
19252 = (1)(2 + 3 + 4 + ... + 12)(13 + 14 + 15 + ... + 37)(38 + 39),
19252 = (1)(2 + 3 + 4 + ... + 8)(9 + 10 + 11 + 12 + 13)(14 + 15 + 16 + ... + 63).

19252 = 93 + 1123 + 1323 = 353 + 853 + 1453.

19252 = (88 + 89 + 90 + 91 + 92)2 + (93 + 94 + 95 + 96 + 97)2 + (98 + 99 + 100 + 101 + 102)2 + ... + (138 + 139 + 140 + 141 + 142)2.

19252 = 3705625 appears in the decimal expressions of π:
  π = 3.14159•••3705625••• (from the 22048th digit)
  (3705625 is the sixth 7-digit square in the expression of π.)

Page of Squares : First Upload March 5, 2007 ; Last Revised November 25, 2008
by Yoshio Mimura, Kobe, Japan

1926

19262 = 3709476, a zigzag square.

19262 = 3! + 3! + 4! + 8! + 8! + 10!.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1927

19272 = 234 + 324 + 324 + 344.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1928

19282 = 3717184, a zigzag square.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1929

1 / 1929 = 0.0005184..., with 5184 = 722.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1930

19302 = 1553 + 45 + 17.

Page of Squares : First Upload January 6, 2011 ; Last Revised January 6, 2011
by Yoshio Mimura, Kobe, Japan

1931

19312 = 443 + 813 + 1463.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1932

19322 = (1)(2)(3)(4 + 5 + 6 + ... + 10)(11 + 12)(13 + 14 + 15 + ... + 35),
19322 = (1 + 2)(3 + 4)(5 + 6 + 7 + ... + 11)(12 + 13 + 14 + ... + 80),
19322 = (1 + 2)(3 + 4)(5 + 6 + 7 + ... + 18)(19 + 20 + 21 + ... + 50),
19322 = (1 + 2)(3 + 4)(5 + 6 + 7 + ... + 27)(28 + 29 + 30 + ... + 41),
19322 = (1 + 2 + 3)(4 + 5 + ... + 10)(11 + 12)(13 + 14 + ... + 35).

19322 = 18 * 19 * 20 + 20 * 21 * 22 + 22 * 23 * 24 + ... + 72 * 73 * 74.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1934

19342 = 3740356, 32 + 72 + 42 + 02 + 32 + 52 + 62 = 122.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1935

A cubic polynomial :
(X + 19352)(X + 26882)(X + 28002) = X3 + 43372X2 + 106327202X + 145635840002.

19352 = (1 + 2)(3)(4 + 5 + 6 + ... + 21)(22 + 23 + 24 + ... + 64).

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1936

The square of 44.

A chain of squares : 1936 > 196 > 16 > 1.

19362 = 3748096, a zigzag square with different digits.

1999396 = 14142, a square pegged by 9.

19362= 112 x 113 + 113 x 114 + 114 x 115 +...+ 232 x 233.

19362 = 163 + 1003 + 1403 = 223 + 443 + 1543.

Page of Squares : First Upload March 5, 2007 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1937

19372 = 3751969, 3 - 7 * 5 + 1969 = 1937.

130k + 1937k + 4264k + 7358k are squares for k = 1,2,3 (1172, 87232, 6950972).

Page of Squares : First Upload March 5, 2007 ; Last Revised May 10, 2011
by Yoshio Mimura, Kobe, Japan

1938

19382 = 14 + 94 + 314 + 414.

The integral triangle of sides 1585, 5274, 6137 (or 1657, 5491, 6570) has square area 19382.

19382 = (62 + 2)(132 + 2)(242 + 2) = (62 + 2)(72 + 2)(442 + 2).

762k + 1938k + 2334k + 3066k are squares for k = 1,2,3 (902, 43802, 2219402).

Page of Squares : First Upload July 14, 2008 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

1940

19402= 789 x 790 + 790 x 791 + 791 x 792 + 792 x 793 + ... + 794 x 795.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1941

19412 = 3767481, a zigzag square.

19412 = 3767481 appears in the decimal expressions of π:
  π = 3.14159•••3767481••• (from the 96853rd digit)

Page of Squares : First Upload March 5, 2007 ; Last Revised November 4, 2008
by Yoshio Mimura, Kobe, Japan

1942

19422 = 3771364, 32 + 72 + 72 + 12 + 32 + 62 + 42 = 132.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1943

19432 = 14 + 244 + 244 + 424.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1944

19442 = 3779136, a square with odd digits except the last digit 6.

19442 = 1083 + 1083 + 1083 = 185 + 185.

452 + 1944 = 632, 452 - 1944 = 92.

Komachi equation: 19442 = 92 * 82 / 72 * 62 / 52 / 42 * 32 * 2102.

19442 = (1)(2)(3)(4)(5 + 6 + 7 + ... + 31)(32 + 33 + 34 + ... + 40),
19442 = (1)(2 + 3 + 4 + ... + 7)(8)(9)(10 + 11 + 12 + ... + 17)(18),
19442 = (1 + 2)(3)(4)(5 + 6 + 7)(8 + 9 + 10 + ... + 16)(17 + 18 + 19),
19442 = (1 + 2 + 3)(4)(5 + 6 + 7 + ... + 31)(32 + 33 + 34 + ... + 40).

Page of Squares : First Upload March 5, 2007 ; Last Revised August 24, 2013
by Yoshio Mimura, Kobe, Japan

1946

Loop of length 14 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
1946 - 2477 - 6505 - 4250 - 4264 - 5860 - 6964 - 8857 - 10993 - 8731 - 8530 - 8125 - 7186 - 12437 - 1946
(Note f(1946) = 192 + 462 = 2477,   f(2477) = 242 + 772 = 6505, etc. See 41)

Page of Squares : First Upload October 9, 2008 ; Last Revised October 9, 2008
by Yoshio Mimura, Kobe, Japan

1947

19472 = 263 + 813 + 1483.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1948

19482 = 84 + 84 + 144 + 444.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1949

19492 = 3798601, a square with different digits.

The sum of consecutive primnes : 3 + 5 + 7 + 11 + 13 + 17 + ... + 1949 = 5132.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1950

The integral triangle of sides 3341, 3466, 6375 has square area 19502.

19502 = (12 + 9)(112 + 9)(542 + 9) = (12 + 9)(22 + 9)(1712 + 9) = (112 + 9)(1712 + 9)
= (22 + 9)(42 + 9)(92 + 9)(112 + 9) = (42 + 9)(92 + 9)(412 + 9).

19502 = (1)(2 + 3)(4 + 5 + 6)(7 + 8 + 9 + ... + 318),
19502 = (1)(2 + 3 + 4 + 5 + 6)(7 + 8 + 9 + ... + 32)(33 + 34 + 35 + ... + 42),
19502 = (1 + 2)(3)(4)(5)(6 + 7)(8 + 9 + 10 + ... + 57),
19502 = (1 + 2 + 3 + ... + 12)(13 + 14 + 15 + ... + 312).

19502= 244 x 245 + 245 x 246 + 246 x 247 + 247 x 248 + 248 x 249 + ... + 295 x 296.

78k + 1092k + 1950k + 10569k are squares for k = 1,2,3 (1172, 108032, 10905572).

Page of Squares : First Upload March 5, 2007 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

1952

19522 = 43 + 243 + 1563 = 124 + 124 + 124 + 444.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1953

19532 = 3814209, a square with different digits.

19532 = 3814209, and 3 * 81 * 4 * 2 + 0 + 9 = 1953.

19532± 2 are primes.

19532 = (63 + 1)(263 + 1).

19532 = 13 + 23 + 33 + 43 + 53 + 63 + ... + 623.

19532 + 19542 + 19552 + ... + 19842 = 19852 + 19862 + 19872 + ... + 20152.

Page of Squares : First Upload March 5, 2007 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe, Japan

1954

S2(1954) = S2(1100) + S2(1830), where S2(n) = 12 + 22 + 32 + ... + n2.

19542 = 363 + 693 + 1513.

Page of Squares : First Upload March 5, 2007 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1956

The square root of 1956 is 44.226..., and 44 = 22 + 22 + 62.

19564 = 14637786276096, and 142 + 62 + 372 + 72 + 82 + 62 + 22 + 72 + 62 + 02 + 92 + 62 = 1956.

Page of Squares : First Upload March 5, 2007 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

1959

19592 = 3837681, a zigzag square.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1961

19612 = 3845521, 32 + 82 + 42 + 52 + 52 + 22 + 12 = 122.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1962

Komachi equations:
19622 = 92 + 82 - 72 + 6542 * 32 + 22 - 102 = - 92 - 82 + 72 + 6542 * 32 - 22 + 102.

Page of Squares : First Upload September 7, 2010 ; Last Revised September 7, 2010
by Yoshio Mimura, Kobe, Japan

1963

19632 = 3853369, and 38 * 53 + 3 - 6 * 9 = 1963.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1964

19642 = 3857296, a zigzag square with different digits.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1966

19662 = 3865156, 32 + 82 + 62 + 52 + 12 + 52 + 62 = 142.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1968

19682 = 503 + 963 + 1423 = 593 + 933 + 1423 = 943 + 1143 + 1163.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1969

13 + 33 + 53 + 73 + 93 + 113 + 133 + 153 + ... + 19693 = 13721052.

19692 = 3876961, 3 * 8 * 7 * 6 + 961 = 1969.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1970

19702 = (12 + 1)(13932 + 1).

Page of Squares : First Upload November 2, 2013 ; Last Revised November 2, 2013
by Yoshio Mimura, Kobe, Japan

1971

19712 = 3884841, 3 + 8 - 8 + 48 * 41 = 3 + 8 / 8 * 48 * 41 = 3 - 8 + 8 + 48 * 41 = 1971
      = 3 * 8 / 8 + 48 * 41 = 3 / 8 * 8 + 48 * 41 = 1971.

Komachi equation: 19712 = 92 * 8762 / 52 * 42 / 322 * 102.

Page of Squares : First Upload March 5, 2007 ; Last Revised September 7, 2010
by Yoshio Mimura, Kobe, Japan

1972

19722 = 3888784, a square pegged by 8.

19722 = 103 + 1083 + 1383.

Page of Squares : First Upload March 5, 2007 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1974

19742 = (32 + 5)(182 + 5)(292 + 5).

Komachi equations:
19742 = 9872 * 62 * 52 * 42 / 32 / 22 / 102 = 9872 * 62 / 52 / 42 / 32 * 22 * 102
 = 9872 / 62 * 52 * 42 * 32 * 22 / 102 = 9872 / 62 / 52 * 42 * 32 / 22 * 102.

Page of Squares : First Upload September 7, 2010 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

1976

19762 = 3904576, a square with different digits.

19762 = (12 + 3)(72 + 3)(1372 + 3).

19762 = 263 + 803 + 1503 = 383 + 1173 + 1313.

19762 = 3904576 appears in the decimal expressions of π:
  π = 3.14159•••3904576••• (from the 74056th digit)

Page of Squares : First Upload March 5, 2007 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

1978

19782± 3 are primes.

19782 = 174 + 194 + 234 + 434.

Page of Squares : First Upload July 14, 2008 ; Last Revised January 16, 2014
by Yoshio Mimura, Kobe, Japan

1980

The integral triangle of sides 1971, 4015, 4706 has square area 19802.

19802 = S2(147) + S2(204), where S2(n) = 12 + 22 + 32 + ... + n2.

19802 = (102 - 1)(1992 - 1).

19802 = (1)(2)(3)(4)(5)(6 + 7 + 8 + ... + 16)(17 + 18 + 19 + ... + 28),
19802 = (1)(2)(3)(4)(5 + 6)(7 + 8)(9)(10)(11),
19802 = (1)(2)(3)(4 + 5)(6 + 7 + 8 + 9 + 10)(11)(12 + 13 + 14 + ... + 21),
19802 = (1)(2)(3 + 4 + 5 + ... + 13)(14 + 15 + 16 + ... + 211),
19802 = (1)(2)(3 + 4 + 5 + 6 + ... + 42)(43 + 44 + 45 + ... + 78),
19802 = (1)(2 + 3)(4)(5)(6)(7 + 8 + 9 + ... + 114),
19802 = (1)(2 + 3)(4)(5 + 6)(7 + 8 + 9 + ... + 15)(16 + 17 + 18 + ... + 24),
19802 = (1)(2 + 3)(4 + 5)(6 + 7 + 8 + ... + 38)(39 + 40 + 41),
19802 = (1)(2 + 3 + 4 + ... + 13)(14 + 15 + 16 + ... + 19)(20 + 21 + 22 + ... + 35),
19802 = (1)(2 + 3 + 4)(5)(6 + 7 + 8 + ... + 38)(39 + 40 + 41),
19802 = (1)(2 + 3 + 4)(5 + 6)(7 + 8 + 9 + ... + 11)(12 + 13 + 14 + ... + 43),
19802 = (1)(2 + 3 + 4)(5 + 6)(7 + 8 + ... + 18)(19 + 20 + ... + 29),
19802 = (1)(2 + 3 + 4)(5 + 6)(7 + 8 + ... + 281),
19802 = (1)(2 + 3 + 4)(5 + 6 + ... + 10)(11)(12 + 13 + ... + 43),
19802 = (1 + 2)(3)(4 + 5 + ... + 36)(37 + 38 + ... + 51),
19802 = (1 + 2)(3)(4 + 5 + ... + 7)(8)(9 + 10 + ... + 13)(14 + 15 + 16),
19802 = (1 + 2)(3 + 4 + ... + 6)(7 + 8 + ... + 17)(18 + 19 + ... + 37),
19802 = (1 + 2)(3 + 4 + 5)(6)(7 + 8 + ... + 26)(27 + 28),
19802 = (1 + 2 + ... + 10)(11 + 12 + 13)(14 + 15 + ... + 19)(20),
19802 = (1 + 2 + ... + 44)(45 + 46 + ... + 99),
19802 = (1 + 2 + ... + 8)(9 + 10 + ... + 13)(14 + 15 + ... + 19)(20),
19802 = (1 + 2 + ... + 8)(9 + 10 + ... + 16)(17 + 18 + ... + 49),
19802 = (1 + 2 + ... + 8)(9 + 10 + 11)(12 + 13 + ... + 21)(22),
19802 = (1 + 2 + 3)(4)(5)(6 + 7 + ... + 16)(17 + 18 + ... + 28),
19802 = (1 + 2 + 3)(4)(5 + 6)(7 + 8)(9)(10)(11),
19802 = (1 + 2 + 3)(4 + 5)(6 + 7 + ... + 10)(11)(12 + 13 + ... + 21).

19802 = 137 x 138 + 139 x 140 + 141 x 142 + 143 x 144 + ... + 295 x 296.

Page of Squares : First Upload March 5, 2007 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

1981

19812 = 3924361, a zigzag square.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1983

19832 = 3932289, 3932 / 2 + 8 + 9 = 1983.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1988

19882 = 143 + 433 + 1573 = 463 + 703 + 1523.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1989

19892 = 3956121, a zigzag square.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1990

19902 = (14 + 15 + 16 + 17 + 18)2 + (19 + 20 + 21 + 22 + 23)2 + (24 + 25 + 26 + 27 + 28)2 + ... + (129 + 130 + 131 + 132 + 133)2.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1991

19912 = 3964081, a square with different digits.

19912 = S2(175) + S2(186), where S2(n) = 12 + 22 + 32 + ... + n2.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1992

19922 = 3968064, a zigzag square.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1993

19932 = 3972049, 3 * 9 * 72 + 0 + 49 = 1993.

19932 = 1223 + 95 + 87.

Page of Squares : First Upload March 5, 2007 ; Last Revised January 6, 2011
by Yoshio Mimura, Kobe, Japan

1995

19952 = (1 + 2)(3 + 4)(5 + 6 + 7 + ... + 14)(15)(16 + 17 + 18 + ... + 22),
19952 = (1 + 2)(3 + 4)(5 + 6 + 7 + 8 + 9)(10 + 11 + 12 + ... + 104),
19952 = (1 + 2 + 3 + ... + 6)(7 + 8 + 9 + ... + 12)(13 + 14 + 15 + ... + 82).

19952 = (12 + 13 + 14)2 + (15 + 16 + 17)2 + (18 + 19 + 20)2 + ... + (156 + 157 + 158)2.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1996

19962 = 3984016, a square with different digits.

Page of Squares : First Upload March 5, 2007 ; Last Revised March 5, 2007
by Yoshio Mimura, Kobe, Japan

1998

19985 = 31840319680159968 : 312 + 82 + 42 + 02 + 32 + 192 + 62 + 82 + 02 + 152 + 92 + 92 + 62 + 82 = 1998.

19982 = 3992004 appears in the decimal expressions of e:
  e = 2.71828•••3992004••• (from the 54972nd digit)

Page of Squares : First Upload November 4, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan