8000
80002 = 383 + 2953 + 3373 = 643 + 2723 + 3523 = 1143 + 2613 + 3553 = 1403 + 2803 + 3403.
Komachi equations: 80002 = 96 * 86 / 76 / 66 / 546 * 36 * 2106.
Page of Squares : First Upload June 16, 2008 ; Last Revised November 9, 2010by Yoshio Mimura, Kobe, Japan
8001
80012 = 504 + 504 + 574 + 804.
80012 + 80022 + 80032 + ... + 80642 = 80652 + 80662 + 80672 + ... + 81272.
Page of Squares : First Upload June 16, 2008 ; Last Revised September 16, 2011by Yoshio Mimura, Kobe, Japan
8002
80022 = 64032004, and 62 + 42 + 02 + 32 + 22 + 02 + 02 + 42 = 92.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8007
80072 = 24 + 384 + 724 + 774.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8010
730k + 3970k + 4190k + 8010k are squares for k = 1,2,3 (1302, 99002, 8065002).
Page of Squares : First Upload July 12, 2011 ; Last Revised July 12, 2011by Yoshio Mimura, Kobe, Japan
8011
80112 = 64176121, and 62 + 42 + 12 + 72 + 62 + 12 + 22 + 12 = 122.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8012
80122 = 64192144 appears in the decimal expressions of e:
e = 2.71828•••64192144••• (from the 21351st digit)
(64192144 is the third 8-digit square in the expression of e.)
by Yoshio Mimura, Kobe, Japan
8014
80145 = 33055725277697177824 :
32 + 302 + 52 + 52 + 72 + 252 + 22 + 72 + 762 + 92 + 72 + 172 + 72 + 82 + 22 + 42 = 8014.
by Yoshio Mimura, Kobe, Japan
8016
The square root of 8016 is 89.532117...., and 89 = 52 + 32 + 22 + 12 + 12 + 72.
80164 = 4128866435137536,
and 42 + 12 + 22 + 882 + 62 + 62 + 42 + 32 + 52 + 12 + 32 + 72 + 52 + 32 + 62 = 8016.
by Yoshio Mimura, Kobe, Japan
8017
80172 = 24 + 314 + 744 + 764 = 314 + 344 + 524 + 864.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8018
80182 = 474 + 614 + 674 + 714.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8019
80192 = 95 + 185 + 185 + 365.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8020
80205 = 33179653126403200000 :
32 + 32 + 12 + 72 + 92 + 652 + 312 + 262 + 402 + 32 + 202 + 02 + 02 + 02 + 02
= 32 + 312 + 72 + 92 + 652 + 32 + 12 + 262 + 402 + 32 + 202 + 02 + 02 + 02 + 02 = 8020.
by Yoshio Mimura, Kobe, Japan
8021
80212 = 64336441, and 6 * 4 * 336 - 44 + 1 = 8021.
80215 = 33200343854823324101 :
332 + 22 + 02 + 02 + 342 + 32 + 82 + 542 + 82 + 22 + 32 + 322 + 412 + 02 + 12
= 32 + 322 + 02 + 02 + 342 + 32 + 82 + 542 + 82 + 22 + 332 + 22 + 412 + 02 + 12 = 8021.
by Yoshio Mimura, Kobe, Japan
8023
80232 = 873 + 3173 + 3173.
80235 = 33241756278080076343 :
32 + 322 + 412 + 72 + 562 + 22 + 72 + 82 + 02 + 82 + 02 + 02 + 72 + 62 + 32 + 432 = 8023.
by Yoshio Mimura, Kobe, Japan
8025
The square root of 8025 is 89.58...., and 89 = 52 + 82.
80855 = 34546187132462053125 :
342 + 542 + 62 + 182 + 72 + 12 + 32 + 242 + 62 + 22 + 02 + 532 + 122 + 52 = 8085.
by Yoshio Mimura, Kobe, Japan
8026
The square root of 8026 is 89.58...., and 89 = 52 + 82.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8027
80272 = 2013 + 2763 + 3283.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8028
80282 = 144 + 524 + 524 + 844.
80284 = 4153645759078656,
and 42 + 12 + 52 + 32 + 62 + 452 + 752 + 92 + 02 + 72 + 82 + 62 + 52 + 62 = 8028.
by Yoshio Mimura, Kobe, Japan
8029
80294 = 4155715725155281 and 42 + 152 + 52 + 72 + 152 + 72 + 252 + 152 + 52 + 22 + 812 = 8029.
Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
8030
80302 = (42 + 6)(17122 + 6).
Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
8031
80312 = 64496961, and 642 + 42 + 92 + 62 + 92 + 612.
Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
8033
The square root of 8033 is 89.627...., and 89 = 62 + 22 + 72.
80332 = 252 + 262 + 272 + 282 + ... + 5782.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8035
80352 = 30 + 31 + 32 + 35 + 36 + 39 + 310 + 311 + 312 + 313 + 314 + 315 + 316.
80354 = 4168151773500625,
and 412 + 62 + 82 + 152 + 12 + 772 + 32 + 52 + 02 + 02 + 62 + 22 + 52 = 8035.
by Yoshio Mimura, Kobe, Japan
8037
80372 = 1503 + 2423 + 3613.
627k + 3667k + 8037k + 10773k are squares for k = 1,2,3 (1522, 139462, 13486962).
Page of Squares : First Upload June 16, 2008 ; Last Revised July 12, 2011by Yoshio Mimura, Kobe, Japan
8040
80402 = (13 + 9)(33 + 9)(53 + 9)(113 + 9).
Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
8041
80412 = 64657681 is a zigzag square.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8048
80482 = 84 + 324 + 444 + 884 = 564 + 644 + 644 + 684.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8049
80492 = 253 + 1763 + 3903.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8051
8051 = (12 + 22 + 32 + ... + 2902) / (12 + 22 + 32 + ... + 142).
Page of Squares : First Upload November 25, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
8056
80562 = 2323 + 2643 + 3243.
80562 = 64899136, and 62 + 42 + 82 + 92 + 92 + 12 + 32 + 62 = 182.
2812k + 4940k + 8056k + 13433k are squares for k = 1,2,3 (1712, 166632, 17577092).
Page of Squares : First Upload June 16, 2008 ; Last Revised July 12, 2011by Yoshio Mimura, Kobe, Japan
8059
80592 = 64947481 is a zigzag square.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8061
80612 = 253 + 1133 + 3993.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8062
80624 = 4224459737272336,
and 42 + 222 + 442 + 592 + 72 + 32 + 72 + 272 + 22 + 32 + 362 = 8062.
by Yoshio Mimura, Kobe, Japan
8064
1302 + 8064 = 1582, 1302 - 8064 = 942.
80642 = (22 - 1)(32 - 1)(132 - 1)(1272 - 1) = (22 - 1)(32 - 1)(172 - 1)(972 - 1)
= (52 - 1)(132 - 1)(1272 - 1) = (52 - 1)(172 - 1)(972 - 1).
80642 = 403 + 1133 + 3993.
Komachi equations: 80642 = 122 / 32 * 42 * 5672 * 82 / 92.
Page of Squares : First Upload June 16, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
8065
The square root of 8065 is 89.805...., and 89 = 82+ 0 2 + 52.
80652 = 65044225, and 6 + 504 * 4 * 2 * 2 - 5 = 8065.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8068
80682 = 244 + 364 + 424 + 884.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8074
80742 = 723 + 1093 + 3993 = 2173 + 2673 + 3303.
The square root of 8074 is 89.85...., and 89 = 82 + 52.
2090k + 8074k + 8558k + 12254k are squares for k = 1,2,3 (1762, 171162, 17327202).
Page of Squares : First Upload June 16, 2008 ; Last Revised July 12, 2011by Yoshio Mimura, Kobe, Japan
8075
80752 = S2(144) + S2(577), where S2(n) = 12 + 22 + 32 + ... + n2.
80752 = 32 + 42 + 52 + 62 + 72 + ... + 5802.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8077
80772 = 65237929, and 62 + 52 + 22 + 32 + 72 + 92 + 22 + 92 = 172.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8079
80794 = 4260204360198081,
and 42 + 22 + 62 + 02 + 22 + 02 + 42 + 362 + 02 + 12 + 92 + 82 + 02 + 812 = 8079.
by Yoshio Mimura, Kobe, Japan
8081
80814 = 4264424473158721,
and 42 + 22 + 642 + 42 + 22 + 42 + 42 + 72 + 32 + 12 + 582 + 72 + 212 = 8081.
by Yoshio Mimura, Kobe, Japan
8082
80822 = 65318724, a square with different digits.
80822 = 1423 + 2253 + 3713.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8084
1 / 8084 = 0.0001237011380504, 122 + 372 + 02 + 112 + 32 + 802 + 52 + 042 = 8084,
1 / 8084 = 0.0001237011380504, 122 + 372 + 0112 + 32 + 802 + 52 + 02 + 42 = 8084,
1 / 8084 = 0.0001237011380504, 122 + 372 + 0112 + 32 + 802 + 52 + 042 = 8084.
by Yoshio Mimura, Kobe, Japan
8085
80852 = (12 + 6)(32 + 6)(272 + 6)(292 + 6) = (12 + 6)(72 + 6)(152 + 6)(272 + 6).
80852 = 493 + 2243 + 3783.
8085 = (12 + 22 + 32 + ... + 492) / (12 + 22).
Page of Squares : First Upload June 16, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
8086
The square root of 8086 is 89.922...., and 89 = 92 + 22 + 22.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8087
80874 = 4277103625385761,
and 42 + 22 + 72 + 72 + 12 + 02 + 362 + 22 + 532 + 82 + 52 + 72 + 612 = 8087.
by Yoshio Mimura, Kobe, Japan
8088
80882 = 783 + 983 + 4003.
80884 = 4279219563073536,
and 42 + 272 + 92 + 22 + 192 + 52 + 632 + 02 + 72 + 32 + 532 + 62 = 8088.
A cubic polynomial
(X + 352)(X + 722)(X + 962) = X3 + 1252X2 + 80882X + 2419202.
by Yoshio Mimura, Kobe, Japan
8089
8089 is the fifth prime for which the Lendre symbol (a/8089) = 1 for a = 1,2,...,16.
80892 = 65431921 appears in the decimal expressions of π:
π = 3.14159•••65431921••• (from the 30043rd digit)
(65431921 is the fourth 8-digit square in the expression of π.)
by Yoshio Mimura, Kobe, Japan
8090
80902 = 65448100, and 6 - 5 * 4 + 4 + 8100 = 8090.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8092
80922 = 344 + 684 + 684 + 684.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan
8094
1065k + 8094k + 14058k + 22152k are squares for k = 1,2,3 (2132, 274772, 37656272).
Page of Squares : First Upload July 12, 2011 ; Last Revised July 12, 2011by Yoshio Mimura, Kobe, Japan
8096
80962 = 65545216, 6 * 5 * 54 * 5 + 2 - 1 * 6 = 6 * 5 * 54 * 5 + 2 * 1 - 6 = 8096.
80962 = (12 + 7)(22 + 7)(132 + 7)(652 + 7) = (12 + 7)(22 + 7)(42 + 7)(92 + 7)(192 + 7)
= (12 + 7)(42 + 7)(192 + 7)(312 + 7) = (22 + 7)(32 + 7)(92 + 7)(652 + 7)
= (32 + 7)(312 + 7)(652 + 7) = (92 + 7)(132 + 7)(652 + 7).
by Yoshio Mimura, Kobe, Japan
8097
80972 = 234 + 484 + 744 + 744.
Page of Squares : First Upload June 16, 2008 ; Last Revised June 16, 2008by Yoshio Mimura, Kobe, Japan