## 1900

1900^{2}± 3 are primes.

1900^{2} = 3610000, and 36 = 6^{2}, 10000 = 100^{2}.

1900^{2} = (1)(2 + 3)(4 + 5 + 6 + ... + 28)(29 + 30 + 31 + ... + 66).

by Yoshio Mimura, Kobe, Japan

## 1902

1902^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 1903

1903^{2} = 3621409, a square with different digits.

by Yoshio Mimura, Kobe, Japan

## 1904

1904^{5} = 25022731752833024 :

25^{2} + 0^{2} + 22^{2} + 7^{2} + 3^{2} + 1^{2} + 7^{2} + 5^{2} + 2^{2} + 8^{2} + 3^{2} + 3^{2} + 0^{2} + 24^{2} = 1904.

by Yoshio Mimura, Kobe, Japan

## 1906

1906^{2} = 3632836, and 3 * 632 - 8 + 3 * 6 = 1906.

by Yoshio Mimura, Kobe, Japan

## 1907

1907^{2} = 3636649, and 3 * 636 - 6 - 4 + 9 = 1907.

1917^{2} = 1! + 1! + 1! + 3! + 6! + 7! + 8! + 10! = 1! + 2! + 3! + 6! + 7! + 8! + 10!.

by Yoshio Mimura, Kobe, Japan

## 1909

1909^{2} = 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.)

by Yoshio Mimura, Kobe, Japan

## 1910

The sum of the divisors of 1910^{2} is a square, 2821^{2}.

by Yoshio Mimura, Kobe, Japan

## 1911

1911^{2} = (6^{2} + 3)(306^{2} + 3).

by Yoshio Mimura, Kobe, Japan

## 1912

1912^{2}± 3 are primes.

1912^{2} = 23^{3} + 81^{3} + 146^{3} = 92^{3} + 102^{3} + 122^{3} = 2^{4} + 22^{4} + 34^{4} + 38^{4}.

by Yoshio Mimura, Kobe, Japan

## 1913

1913^{2} = 3659569, 3 * 659 + 5 - 69 = 1913.

by Yoshio Mimura, Kobe, Japan

## 1914

1914^{2} = 3663396, a square with jst 3 kinds of digits.

by Yoshio Mimura, Kobe, Japan

## 1916

1916^{2} = 3671056 appears in the decimal expressions of e:

e = 2.71828•••3671056••• (from the 50873rd digit)

by Yoshio Mimura, Kobe, Japan

## 1917

1917^{2} = 36^{3} + 36^{3} + 153^{3} = 36^{3} + 114^{3} + 129^{3} = 54^{3} + 81^{3} + 144^{3}.

by Yoshio Mimura, Kobe, Japan

## 1918

1918^{2} = 3678724 appears in the decimal expressions of e:

e = 2.71828•••3678724••• (from the 54950th digit)

by Yoshio Mimura, Kobe, Japan

## 1920

A cubic polynomial :

(X + 1920^{2})(X + 2737^{2})(X + 3600^{2}) = X^{3} + 4913^{2}X^{2} + 13133040^{2}X + 18918144000^{2}.

1920^{2} = 3686400, and 36 * 8 / 6 * 40 + 0 = 1920.

1920^{2} = 6! + 6! + 6! + 7! + 7! + 7! + 8! + 10!.

1920^{2} = (3^{2} - 1)(7^{2} - 1)(9^{2} - 1)(11^{2} - 1) = (7^{2} - 1)(9^{2} - 1)(31^{2} - 1).

1920^{2} = 10^{3} + 47^{3} + 153^{3} = 40^{3} + 48^{3} + 152^{3}.

52^{2} + 1920 = 68^{2}, 52^{2} - 1920 = 28^{2}.

by Yoshio Mimura, Kobe, Japan

## 1921

1921^{2} = 3690241, a square with differential digits.

1921^{2} = 25^{4} + 30^{4} + 30^{4} + 36^{4}.

by Yoshio Mimura, Kobe, Japan

## 1922

1922^{2} = 11^{4} + 19^{4} + 19^{4} + 43^{4} = 31^{4} + 31^{4} + 31^{4} + 31^{4}.

by Yoshio Mimura, Kobe, Japan

## 1924

1924^{2}± 3 are primes.

1924^{2} = 24^{4} + 30^{4} + 40^{4}.

by Yoshio Mimura, Kobe, Japan

## 1925

1925 = (1^{2} + 2^{2} + 3^{2} + ... + 1287^{2}) / (1^{2} + 2^{2} + 3^{2} + ... + 103^{2}).

1925^{2} = (1)(2 + 3 + 4 + ... + 12)(13 + 14 + 15 + ... + 22)(23 + 24 + 25 + ... + 32),

1925^{2} = (1)(2 + 3 + 4 + ... + 12)(13 + 14 + 15 + ... + 37)(38 + 39),

1925^{2} = (1)(2 + 3 + 4 + ... + 8)(9 + 10 + 11 + 12 + 13)(14 + 15 + 16 + ... + 63).

1925^{2} = 9^{3} + 112^{3} + 132^{3} = 35^{3} + 85^{3} + 145^{3}.

1925^{2} = (88 + 89 + 90 + 91 + 92)^{2} + (93 + 94 + 95 + 96 + 97)^{2} + (98 + 99 + 100 + 101 + 102)^{2} + ... + (138 + 139 + 140 + 141 + 142)^{2}.

1925^{2} = 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.)

by Yoshio Mimura, Kobe, Japan

## 1926

1926^{2} = 3709476, a zigzag square.

1926^{2} = 3! + 3! + 4! + 8! + 8! + 10!.

by Yoshio Mimura, Kobe, Japan

## 1927

1927^{2} = 23^{4} + 32^{4} + 32^{4} + 34^{4}.

by Yoshio Mimura, Kobe, Japan

## 1928

1928^{2} = 3717184, a zigzag square.

by Yoshio Mimura, Kobe, Japan

## 1929

1 / 1929 = 0.0005184..., with 5184 = 72^{2}.

by Yoshio Mimura, Kobe, Japan

## 1930

1930^{2} = 155^{3} + 4^{5} + 1^{7}.

by Yoshio Mimura, Kobe, Japan

## 1931

1931^{2} = 44^{3} + 81^{3} + 146^{3}.

by Yoshio Mimura, Kobe, Japan

## 1932

1932^{2} = (1)(2)(3)(4 + 5 + 6 + ... + 10)(11 + 12)(13 + 14 + 15 + ... + 35),

1932^{2} = (1 + 2)(3 + 4)(5 + 6 + 7 + ... + 11)(12 + 13 + 14 + ... + 80),

1932^{2} = (1 + 2)(3 + 4)(5 + 6 + 7 + ... + 18)(19 + 20 + 21 + ... + 50),

1932^{2} = (1 + 2)(3 + 4)(5 + 6 + 7 + ... + 27)(28 + 29 + 30 + ... + 41),

1932^{2} = (1 + 2 + 3)(4 + 5 + ... + 10)(11 + 12)(13 + 14 + ... + 35).

1932^{2} = 18 * 19 * 20 + 20 * 21 * 22 + 22 * 23 * 24 + ... + 72 * 73 * 74.

by Yoshio Mimura, Kobe, Japan

## 1934

1934^{2} = 3740356, 3^{2} + 7^{2} + 4^{2} + 0^{2} + 3^{2} + 5^{2} + 6^{2} = 12^{2}.

by Yoshio Mimura, Kobe, Japan

## 1935

A cubic polynomial :

(X + 1935^{2})(X + 2688^{2})(X + 2800^{2}) = X^{3} + 4337^{2}X^{2} + 10632720^{2}X + 14563584000^{2}.

1935^{2} = (1 + 2)(3)(4 + 5 + 6 + ... + 21)(22 + 23 + 24 + ... + 64).

by Yoshio Mimura, Kobe, Japan

## 1936

The square of 44.

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

1936^{2} = 3748096, a zigzag square with different digits.

1999396 = 1414^{2}, a square pegged by 9.

1936^{2}= 112 x 113 + 113 x 114 + 114 x 115 +...+ 232 x 233.

1936^{2} = 16^{3} + 100^{3} + 140^{3} = 22^{3} + 44^{3} + 154^{3}.

by Yoshio Mimura, Kobe, Japan

## 1937

1937^{2} = 3751969, 3 - 7 * 5 + 1969 = 1937.

130^{k} + 1937^{k} + 4264^{k} + 7358^{k} are squares for k = 1,2,3 (117^{2}, 8723^{2}, 695097^{2}).

by Yoshio Mimura, Kobe, Japan

## 1938

1938^{2} = 1^{4} + 9^{4} + 31^{4} + 41^{4}.

The integral triangle of sides 1585, 5274, 6137 (or 1657, 5491, 6570) has square area 1938^{2}.

1938^{2} = (6^{2} + 2)(13^{2} + 2)(24^{2} + 2) = (6^{2} + 2)(7^{2} + 2)(44^{2} + 2).

762^{k} + 1938^{k} + 2334^{k} + 3066^{k} are squares for k = 1,2,3 (90^{2}, 4380^{2}, 221940^{2}).

by Yoshio Mimura, Kobe, Japan

## 1940

1940^{2}= 789 x 790 + 790 x 791 + 791 x 792 + 792 x 793 + ... + 794 x 795.

by Yoshio Mimura, Kobe, Japan

## 1941

1941^{2} = 3767481, a zigzag square.

1941^{2} = 3767481 appears in the decimal expressions of π:

π = 3.14159•••3767481••• (from the 96853rd digit)

by Yoshio Mimura, Kobe, Japan

## 1942

1942^{2} = 3771364, 3^{2} + 7^{2} + 7^{2} + 1^{2} + 3^{2} + 6^{2} + 4^{2} = 13^{2}.

by Yoshio Mimura, Kobe, Japan

## 1943

1943^{2} = 1^{4} + 24^{4} + 24^{4} + 42^{4}.

by Yoshio Mimura, Kobe, Japan

## 1944

1944^{2} = 3779136, a square with odd digits except the last digit 6.

1944^{2} = 108^{3} + 108^{3} + 108^{3} = 18^{5} + 18^{5}.

45^{2} + 1944 = 63^{2}, 45^{2} - 1944 = 9^{2}.

Komachi equation: 1944^{2} = 9^{2} * 8^{2} / 7^{2} * 6^{2} / 5^{2} / 4^{2} * 3^{2} * 210^{2}.

1944^{2} = (1)(2)(3)(4)(5 + 6 + 7 + ... + 31)(32 + 33 + 34 + ... + 40),

1944^{2} = (1)(2 + 3 + 4 + ... + 7)(8)(9)(10 + 11 + 12 + ... + 17)(18),

1944^{2} = (1 + 2)(3)(4)(5 + 6 + 7)(8 + 9 + 10 + ... + 16)(17 + 18 + 19),

1944^{2} = (1 + 2 + 3)(4)(5 + 6 + 7 + ... + 31)(32 + 33 + 34 + ... + 40).

by Yoshio Mimura, Kobe, Japan

## 1946

Loop of length 14 by the function f(N) = ... + c^{2} + b^{2} + a^{2} where N = ... + 100^{2}c + 100b + a:

1946 - 2477 - 6505 - 4250 - 4264 - 5860 - 6964 - 8857 - 10993 - 8731 - 8530 - 8125 - 7186 - 12437 - 1946

(Note f(1946) = 19^{2} + 46^{2} = 2477, f(2477) = 24^{2} + 77^{2} = 6505, etc. See 41)

by Yoshio Mimura, Kobe, Japan

## 1947

1947^{2} = 26^{3} + 81^{3} + 148^{3}.

by Yoshio Mimura, Kobe, Japan

## 1948

1948^{2} = 8^{4} + 8^{4} + 14^{4} + 44^{4}.

by Yoshio Mimura, Kobe, Japan

## 1949

1949^{2} = 3798601, a square with different digits.

The sum of consecutive primnes : 3 + 5 + 7 + 11 + 13 + 17 + ... + 1949 = 513^{2}.

by Yoshio Mimura, Kobe, Japan

## 1950

The integral triangle of sides 3341, 3466, 6375 has square area 1950^{2}.

1950^{2} = (1^{2} + 9)(11^{2} + 9)(54^{2} + 9) = (1^{2} + 9)(2^{2} + 9)(171^{2} + 9) = (11^{2} + 9)(171^{2} + 9)

= (2^{2} + 9)(4^{2} + 9)(9^{2} + 9)(11^{2} + 9) = (4^{2} + 9)(9^{2} + 9)(41^{2} + 9).

1950^{2} = (1)(2 + 3)(4 + 5 + 6)(7 + 8 + 9 + ... + 318),

1950^{2} = (1)(2 + 3 + 4 + 5 + 6)(7 + 8 + 9 + ... + 32)(33 + 34 + 35 + ... + 42),

1950^{2} = (1 + 2)(3)(4)(5)(6 + 7)(8 + 9 + 10 + ... + 57),

1950^{2} = (1 + 2 + 3 + ... + 12)(13 + 14 + 15 + ... + 312).

1950^{2}= 244 x 245 + 245 x 246 + 246 x 247 + 247 x 248 + 248 x 249 + ... + 295 x 296.

78^{k} + 1092^{k} + 1950^{k} + 10569^{k} are squares for k = 1,2,3 (117^{2}, 10803^{2}, 1090557^{2}).

by Yoshio Mimura, Kobe, Japan

## 1952

1952^{2} = 4^{3} + 24^{3} + 156^{3} = 12^{4} + 12^{4} + 12^{4} + 44^{4}.

by Yoshio Mimura, Kobe, Japan

## 1953

1953^{2} = 3814209, a square with different digits.

1953^{2} = 3814209, and 3 * 81 * 4 * 2 + 0 + 9 = 1953.

1953^{2}± 2 are primes.

1953^{2} = (6^{3} + 1)(26^{3} + 1).

1953^{2} = 1^{3} + 2^{3} + 3^{3} + 4^{3} + 5^{3} + 6^{3} + ... + 62^{3}.

1953^{2} + 1954^{2} + 1955^{2} + ... + 1984^{2} = 1985^{2} + 1986^{2} + 1987^{2} + ... + 2015^{2}.

by Yoshio Mimura, Kobe, Japan

## 1954

S_{2}(1954) = S_{2}(1100) + S_{2}(1830), where S_{2}(n) = 1^{2} + 2^{2} + 3^{2} + ... + n^{2}.

1954^{2} = 36^{3} + 69^{3} + 151^{3}.

by Yoshio Mimura, Kobe, Japan

## 1956

The square root of 1956 is 44.226..., and 44 = 2^{2} + 2^{2} + 6^{2}.

1956^{4} = 14637786276096, and 14^{2} + 6^{2} + 37^{2} + 7^{2} + 8^{2} + 6^{2} + 2^{2} + 7^{2} + 6^{2} + 0^{2} + 9^{2} + 6^{2} = 1956.

by Yoshio Mimura, Kobe, Japan

## 1959

1959^{2} = 3837681, a zigzag square.

by Yoshio Mimura, Kobe, Japan

## 1961

1961^{2} = 3845521, 3^{2} + 8^{2} + 4^{2} + 5^{2} + 5^{2} + 2^{2} + 1^{2} = 12^{2}.

by Yoshio Mimura, Kobe, Japan

## 1962

Komachi equations:

1962^{2} = 9^{2} + 8^{2} - 7^{2} + 654^{2} * 3^{2} + 2^{2} - 10^{2} = - 9^{2} - 8^{2} + 7^{2} + 654^{2} * 3^{2} - 2^{2} + 10^{2}.

by Yoshio Mimura, Kobe, Japan

## 1963

1963^{2} = 3853369, and 38 * 53 + 3 - 6 * 9 = 1963.

by Yoshio Mimura, Kobe, Japan

## 1964

1964^{2} = 3857296, a zigzag square with different digits.

by Yoshio Mimura, Kobe, Japan

## 1966

1966^{2} = 3865156, 3^{2} + 8^{2} + 6^{2} + 5^{2} + 1^{2} + 5^{2} + 6^{2} = 14^{2}.

by Yoshio Mimura, Kobe, Japan

## 1968

1968^{2} = 50^{3} + 96^{3} + 142^{3} = 59^{3} + 93^{3} + 142^{3} = 94^{3} + 114^{3} + 116^{3}.

by Yoshio Mimura, Kobe, Japan

## 1969

1^{3} + 3^{3} + 5^{3} + 7^{3} + 9^{3} + 11^{3} + 13^{3} + 15^{3} + ... + 1969^{3} = 1372105^{2}.

1969^{2} = 3876961, 3 * 8 * 7 * 6 + 961 = 1969.

by Yoshio Mimura, Kobe, Japan

## 1970

1970^{2} = (1^{2} + 1)(1393^{2} + 1).

by Yoshio Mimura, Kobe, Japan

## 1971

1971^{2} = 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: 1971^{2} = 9^{2} * 876^{2} / 5^{2} * 4^{2} / 32^{2} * 10^{2}.

by Yoshio Mimura, Kobe, Japan

## 1972

1972^{2} = 3888784, a square pegged by 8.

1972^{2} = 10^{3} + 108^{3} + 138^{3}.

by Yoshio Mimura, Kobe, Japan

## 1974

1974^{2} = (3^{2} + 5)(18^{2} + 5)(29^{2} + 5).

Komachi equations:

1974^{2} = 987^{2} * 6^{2} * 5^{2} * 4^{2} / 3^{2} / 2^{2} / 10^{2} = 987^{2} * 6^{2} / 5^{2} / 4^{2} / 3^{2} * 2^{2} * 10^{2}

= 987^{2} / 6^{2} * 5^{2} * 4^{2} * 3^{2} * 2^{2} / 10^{2} = 987^{2} / 6^{2} / 5^{2} * 4^{2} * 3^{2} / 2^{2} * 10^{2}.

by Yoshio Mimura, Kobe, Japan

## 1976

1976^{2} = 3904576, a square with different digits.

1976^{2} = (1^{2} + 3)(7^{2} + 3)(137^{2} + 3).

1976^{2} = 26^{3} + 80^{3} + 150^{3} = 38^{3} + 117^{3} + 131^{3}.

1976^{2} = 3904576 appears in the decimal expressions of π:

π = 3.14159•••3904576••• (from the 74056th digit)

by Yoshio Mimura, Kobe, Japan

## 1978

1978^{2}± 3 are primes.

1978^{2} = 17^{4} + 19^{4} + 23^{4} + 43^{4}.

by Yoshio Mimura, Kobe, Japan

## 1980

The integral triangle of sides 1971, 4015, 4706 has square area 1980^{2}.

1980^{2} = S_{2}(147) + S_{2}(204), where S_{2}(n) = 1^{2} + 2^{2} + 3^{2} + ... + n^{2}.

1980^{2} = (10^{2} - 1)(199^{2} - 1).

1980^{2} = (1)(2)(3)(4)(5)(6 + 7 + 8 + ... + 16)(17 + 18 + 19 + ... + 28),

1980^{2} = (1)(2)(3)(4)(5 + 6)(7 + 8)(9)(10)(11),

1980^{2} = (1)(2)(3)(4 + 5)(6 + 7 + 8 + 9 + 10)(11)(12 + 13 + 14 + ... + 21),

1980^{2} = (1)(2)(3 + 4 + 5 + ... + 13)(14 + 15 + 16 + ... + 211),

1980^{2} = (1)(2)(3 + 4 + 5 + 6 + ... + 42)(43 + 44 + 45 + ... + 78),

1980^{2} = (1)(2 + 3)(4)(5)(6)(7 + 8 + 9 + ... + 114),

1980^{2} = (1)(2 + 3)(4)(5 + 6)(7 + 8 + 9 + ... + 15)(16 + 17 + 18 + ... + 24),

1980^{2} = (1)(2 + 3)(4 + 5)(6 + 7 + 8 + ... + 38)(39 + 40 + 41),

1980^{2} = (1)(2 + 3 + 4 + ... + 13)(14 + 15 + 16 + ... + 19)(20 + 21 + 22 + ... + 35),

1980^{2} = (1)(2 + 3 + 4)(5)(6 + 7 + 8 + ... + 38)(39 + 40 + 41),

1980^{2} = (1)(2 + 3 + 4)(5 + 6)(7 + 8 + 9 + ... + 11)(12 + 13 + 14 + ... + 43),

1980^{2} = (1)(2 + 3 + 4)(5 + 6)(7 + 8 + ... + 18)(19 + 20 + ... + 29),

1980^{2} = (1)(2 + 3 + 4)(5 + 6)(7 + 8 + ... + 281),

1980^{2} = (1)(2 + 3 + 4)(5 + 6 + ... + 10)(11)(12 + 13 + ... + 43),

1980^{2} = (1 + 2)(3)(4 + 5 + ... + 36)(37 + 38 + ... + 51),

1980^{2} = (1 + 2)(3)(4 + 5 + ... + 7)(8)(9 + 10 + ... + 13)(14 + 15 + 16),

1980^{2} = (1 + 2)(3 + 4 + ... + 6)(7 + 8 + ... + 17)(18 + 19 + ... + 37),

1980^{2} = (1 + 2)(3 + 4 + 5)(6)(7 + 8 + ... + 26)(27 + 28),

1980^{2} = (1 + 2 + ... + 10)(11 + 12 + 13)(14 + 15 + ... + 19)(20),

1980^{2} = (1 + 2 + ... + 44)(45 + 46 + ... + 99),

1980^{2} = (1 + 2 + ... + 8)(9 + 10 + ... + 13)(14 + 15 + ... + 19)(20),

1980^{2} = (1 + 2 + ... + 8)(9 + 10 + ... + 16)(17 + 18 + ... + 49),

1980^{2} = (1 + 2 + ... + 8)(9 + 10 + 11)(12 + 13 + ... + 21)(22),

1980^{2} = (1 + 2 + 3)(4)(5)(6 + 7 + ... + 16)(17 + 18 + ... + 28),

1980^{2} = (1 + 2 + 3)(4)(5 + 6)(7 + 8)(9)(10)(11),

1980^{2} = (1 + 2 + 3)(4 + 5)(6 + 7 + ... + 10)(11)(12 + 13 + ... + 21).

1980^{2} = 137 x 138 + 139 x 140 + 141 x 142 + 143 x 144 + ... + 295 x 296.

by Yoshio Mimura, Kobe, Japan

## 1981

1981^{2} = 3924361, a zigzag square.

by Yoshio Mimura, Kobe, Japan

## 1983

1983^{2} = 3932289, 3932 / 2 + 8 + 9 = 1983.

by Yoshio Mimura, Kobe, Japan

## 1988

1988^{2} = 14^{3} + 43^{3} + 157^{3} = 46^{3} + 70^{3} + 152^{3}.

by Yoshio Mimura, Kobe, Japan

## 1989

1989^{2} = 3956121, a zigzag square.

by Yoshio Mimura, Kobe, Japan

## 1990

1990^{2} = (14 + 15 + 16 + 17 + 18)^{2} + (19 + 20 + 21 + 22 + 23)^{2} + (24 + 25 + 26 + 27 + 28)^{2} + ... + (129 + 130 + 131 + 132 + 133)^{2}.

by Yoshio Mimura, Kobe, Japan

## 1991

1991^{2} = 3964081, a square with different digits.

1991^{2} = S_{2}(175) + S_{2}(186), where S_{2}(n) = 1^{2} + 2^{2} + 3^{2} + ... + n^{2}.

by Yoshio Mimura, Kobe, Japan

## 1992

1992^{2} = 3968064, a zigzag square.

by Yoshio Mimura, Kobe, Japan

## 1993

1993^{2} = 3972049, 3 * 9 * 72 + 0 + 49 = 1993.

1993^{2} = 122^{3} + 9^{5} + 8^{7}.

by Yoshio Mimura, Kobe, Japan

## 1995

1995^{2} = (1 + 2)(3 + 4)(5 + 6 + 7 + ... + 14)(15)(16 + 17 + 18 + ... + 22),

1995^{2} = (1 + 2)(3 + 4)(5 + 6 + 7 + 8 + 9)(10 + 11 + 12 + ... + 104),

1995^{2} = (1 + 2 + 3 + ... + 6)(7 + 8 + 9 + ... + 12)(13 + 14 + 15 + ... + 82).

1995^{2} = (12 + 13 + 14)^{2} + (15 + 16 + 17)^{2} + (18 + 19 + 20)^{2} + ... + (156 + 157 + 158)^{2}.

by Yoshio Mimura, Kobe, Japan

## 1996

1996^{2} = 3984016, a square with different digits.

by Yoshio Mimura, Kobe, Japan

## 1998

1998^{5} = 31840319680159968 : 31^{2} + 8^{2} + 4^{2} + 0^{2} + 3^{2} + 19^{2} + 6^{2} + 8^{2} + 0^{2} + 15^{2} + 9^{2} + 9^{2} + 6^{2} + 8^{2} = 1998.

1998^{2} = 3992004 appears in the decimal expressions of e:

e = 2.71828•••3992004••• (from the 54972nd digit)

by Yoshio Mimura, Kobe, Japan