8400
84002 = 70560000, 70 / 5 * 600 + 0 + 0 = 70 / 5 * 600 + 0 * 0 = 8400.
84002 = (22 - 1)(492 - 1)(992 - 1) = (42 - 1)(62 - 1)(92 - 1)(412 - 1) = (62 - 1)(292 - 1)(492 - 1).
84002 = 53 + 3153 + 3403 = 323 + 843 + 4123 = 2483 + 2523 + 3403.
56 + 8400 = 1552, 56 - 8400 = 852.
The integral triangle of sides 7241, 19509, 20500 has square area 84002.
Komachi equations: 84002 = 92 / 82 * 72 / 62 * 52 * 42 * 322 * 102.
Page of Squares : First Upload July 14, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
8402
84022 = 34 + 474 + 694 + 814 = 474 + 674 + 674 + 714.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8405
84052 = 413 + 3283 + 3283.
84052 = 70644025, and 70 * 6 / 4 * 40 * 2 + 5 = 8405.
84052 = (103 + 104 + 105 + ... + 143)2 + (144 + 145 + 146 + ... + 184)2 + (185 + 186 + 187 + ... + 225)2 + ... + (144 + 145 + 146 + ... + 184)2.
84055 = 41945810344226253125 :
412 + 92 + 452 + 82 + 12 + 02 + 32 + 42 + 42 + 22 + 22 + 622 + 52 + 32 + 12 + 252 = 8405.
by Yoshio Mimura, Kobe, Japan
8406
84062± 5 are primes.
84065 = 41970769173904039776 :
42 + 12 + 92 + 702 + 72 + 62 + 92 + 12 + 72 + 392 + 02 + 42 + 02 + 392 + 72 + 72 + 62 = 8406.
by Yoshio Mimura, Kobe, Japan
8407
84074 = 4995330068167201,
and 492 + 92 + 52 + 32 + 302 + 02 + 62 + 82 + 12 + 672 + 202 + 12 = 8407.
by Yoshio Mimura, Kobe, Japan
8408
84082± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
8409
84092 = 70711281, and 72 + 02 + 72 + 12 + 12 + 22 + 82 + 12 = 132.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8410
84102 = (122 + 1)(172 + 1)(412 + 1).
Page of Squares : First Upload November 2, 2013 ; Last Revised November 2, 2013by Yoshio Mimura, Kobe, Japan
8411
1 / 8411 = 0.000118891, 12 + 12 + 82 + 82 + 912 = 8411.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8415
84152 = 1373 + 1923 + 3943.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8416
84162 = 70829056, and 70 + 8290 + 56 = 8416.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8417
1330k + 8417k + 8626k + 10868k are squares for k = 1,2,3 (1712, 162832, 15887612).
84175 = 42246101280682101857 :
42 + 22 + 242 + 62 + 12 + 02 + 12 + 282 + 02 + 62 + 822 + 102 + 12 + 82 + 52 + 72
= 42 + 22 + 242 + 62 + 102 + 12 + 282 + 02 + 62 + 822 + 12 + 02 + 12 + 82 + 52 + 72 = 8417.
by Yoshio Mimura, Kobe, Japan
8419
84192 = 70879561, a zigzag square.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8421
84212 = 70913241, a zigzag square.
84212 = 493 + 2423 + 3843.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8424
84242 = 183 + 4143.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8425
84252 = 93 + 283 + 4143 = 93 + 2803 + 3663 = 454 + 604 + 604 + 804.
84252 = 70980625, and 70 * 9 * 80 / 6 + 25 = 8425.
84255 = 42447248881416015625 :
422 + 42 + 42 + 72 + 242 + 82 + 82 + 82 + 12 + 412 + 62 + 02 + 152 + 622 + 52
= 422 + 442 + 72 + 242 + 82 + 82 + 82 + 12 + 42 + 12 + 602 + 152 + 62 + 22 + 52 = 8425.
by Yoshio Mimura, Kobe, Japan
8426
84262 = 70997476, and 72 + 02 + 92 + 92 + 72 + 42 + 72 + 62 = 192.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8428
84282 = 1403 + 2943 + 3503.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8429
84292 = 173 + 443 + 4143.
84295 = 42548109591244713149 :
42 + 22 + 52 + 42 + 82 + 102 + 92 + 592 + 12 + 22 + 42 + 472 + 12 + 32 + 12 + 492
= 42 + 22 + 52 + 482 + 12 + 02 + 92 + 592 + 12 + 22 + 42 + 472 + 12 + 32 + 142 + 92 = 8429.
by Yoshio Mimura, Kobe, Japan
8432
84322 = 1343 + 1963 + 3943.
84322 = 71098624, a square with different digits.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8436
84362 = 93 + 2923 + 3593 = 743 + 1633 + 4053 = 2013 + 2563 + 3593.
84365 = 42725077122917938176 :
42 + 22 + 72 + 22 + 52 + 02 + 72 + 72 + 122 + 22 + 92 + 12 + 792 + 382 + 172 + 62 = 8436.
by Yoshio Mimura, Kobe, Japan
8437
84372 = 263 + 2013 + 3983.
8437k + 10153k + 30745k + 32461k are squares for k = 1,2,3 (2862, 466182, 80569062).
84375 = 42750406193300905957 :
42 + 22 + 72 + 52 + 02 + 42 + 02 + 612 + 92 + 332 + 02 + 02 + 92 + 02 + 52 + 92 + 572 = 8437.
by Yoshio Mimura, Kobe, Japan
8439
84392 = 71216721, and 7 * 1216 - 72 - 1 = 8439.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8442
84422 = 71267364, and 7 * 1 * 2 * 67 * 36 / 4 = 8442.
84422 = (12 + 5)(22 + 5)(142 + 5)(812 + 5) = (12 + 5)(42 + 5)(142 + 5)(532 + 5)
= (112 + 5)(142 + 5)(532 + 5) = (22 + 5)(32 + 5)(142 + 5)(532 + 5) = (72 + 5)(142 + 5)(812 + 5).
by Yoshio Mimura, Kobe, Japan
8443
84432 = 71284249, and 7 + 1 + 2 + 8424 + 9 = 8443.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8446
The square root of 8446 is 91.902121...., and 91 = 92 + 02 + 22 + 12 + 22 + 12.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8448
The square root of 8448 is 91.913...., and 91 = 92 + 12 + 32.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8450
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
8450 - 9556 - 12161 - 4163 - ... - 9881 - 16165 - 7947 - 8450
(Note f(8450) = 842 + 502 = 9556, f(9556) = 952 + 562 = 12161, etc. See 41)
84502 = (12 + 4)(32 + 4)(292 + 4)(362 + 4) = (22 + 9)(42 + 9)(112 + 9)(412 + 9).
84502 = 1043 + 1693 + 4033 = 654 + 654 + 654 + 654.
84505 = 43080778702812500000 :
42 + 32 + 02 + 82 + 02 + 72 + 72 + 872 + 02 + 22 + 82 + 12 + 252 + 02 + 02 + 02 + 02 + 02 = 8450.
by Yoshio Mimura, Kobe, Japan
8451
84515 = 43106276322069067251 :
42 + 32 + 12 + 02 + 62 + 272 + 62 + 32 + 22 + 202 + 62 + 92 + 02 + 672 + 22 + 512 = 8451.
by Yoshio Mimura, Kobe, Japan
8453
84532 = 71453209, a square with different digits.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8454
84545 = 43182841624825917024 :
432 + 12 + 82 + 22 + 82 + 42 + 12 + 62 + 22 + 482 + 22 + 592 + 12 + 72 + 02 + 242
= 42 + 32 + 12 + 82 + 282 + 412 + 62 + 22 + 482 + 22 + 592 + 12 + 72 + 02 + 22 + 42 = 8454.
by Yoshio Mimura, Kobe, Japan
8455
84555 = 43208387555029534375 :
42 + 32 + 22 + 02 + 832 + 82 + 72 + 52 + 52 + 52 + 02 + 22 + 92 + 52 + 342 + 32 + 72 + 52 = 8455.
by Yoshio Mimura, Kobe, Japan
8457
84572 = 71520849, a square with different digits.
84572 = 34 + 644 + 684 + 764.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8458
1 / 8458 = 0.0001182312603452, 12 + 182 + 232 + 122 + 602 + 342 + 522 = 8458.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8459
84594 = 5120072373011761,
and 512 + 202 + 02 + 722 + 32 + 72 + 32 + 02 + 112 + 72 + 62 + 12 = 8459.
by Yoshio Mimura, Kobe, Japan
8462
84622± 3 are primes.
84625 = 43387547783519044832 :
42 + 332 + 82 + 72 + 52 + 42 + 72 + 72 + 82 + 32 + 52 + 12 + 92 + 02 + 42 + 42 + 832 + 22
= 42 + 332 + 82 + 72 + 52 + 42 + 72 + 72 + 832 + 52 + 12 + 92 + 02 + 42 + 42 + 82 + 32 + 22 = 8462.
by Yoshio Mimura, Kobe, Japan
8463
1 / 8463 = 0.00011816140848, 112 + 812 + 62 + 12 + 402 + 82 + 42 + 82 = 8463.
84632 = 1783 + 3123 + 3293 = 2733 + 2783 + 3103.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8464
The square of 92.
8464 = 922, a zigzag square. and 84642 = 71639296, a zigzag square.
84642 = (42 + 7)(272 + 7)(652 + 7).
84642 = 923 + 2763 + 3683.
Page of Squares : First Upload July 14, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
8465
84652 = 1883 + 2763 + 3533.
84655 = 43464512430286540625 :
42 + 32 + 42 + 62 + 42 + 52 + 122 + 42 + 32 + 02 + 22 + 82 + 652 + 42 + 02 + 622 + 52 = 8465.
by Yoshio Mimura, Kobe, Japan
8466
84662 = (92 + 2)(102 + 2)(922 + 2).
8466k + 14178k + 27438k + 43554k are squares for k = 1,2,3 (3062, 540602, 103311722).
Page of Squares : First Upload July 12, 2011 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
8468
84682 = 2203 + 2993 + 3253.
84685 = 43541586259650925568 :
432 + 52 + 42 + 12 + 52 + 82 + 62 + 252 + 92 + 62 + 502 + 92 + 22 + 552 + 62 + 82 = 8468.
by Yoshio Mimura, Kobe, Japan
8470
84702 = (12 + 6)(22 + 6)(42 + 6)(72 + 6)(292 + 6) = (12 + 6)(42 + 6)(72 + 6)(922 + 6)
= (22 + 6)(292 + 6)(922 + 6) = (42 + 6)(292 + 6)(622 + 6) = (42 + 6)(72 + 6)(82 + 6)(292 + 6).
84702 = (6+ 7 + 8 + ... + 16)2 + (17 + 18 + 19 + ... + 27)2 + (28 + 29 + 30 + ... + 38)2 + ... + (259 + 260 + 261 + ... + 269)2.
Page of Squares : First Upload July 14, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
8472
84725 = 43644521405785669632 :
42 + 32 + 642 + 42 + 52 + 22 + 12 + 42 + 02 + 52 + 72 + 82 + 52 + 62 + 62 + 92 + 632 + 22 = 8472.
by Yoshio Mimura, Kobe, Japan
8474
84742 = 71808676, a zigzag square.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8475
84752 = S2(25) + S2(599), where S2(n) = 12 + 22 + 32 + 42 + ... + n2.
8475, 8476, 8477 and 8478 are four consecutive integers having square factors (the 4th case).
Page of Squares : First Upload November 10, 2008 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
8476
84764 = 5161355726315776,
and 52 + 12 + 62 + 132 + 52 + 572 + 262 + 312 + 572 + 72 + 62 = 8476.
by Yoshio Mimura, Kobe, Japan
8477
84772 = 633 + 3153 + 3433 = 1123 + 2173 + 3923.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8478
84782 = 713 + 1723 + 4053 = 1353 + 1443 + 4053.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8479
84795 = 43825126295938858399 :
42 + 32 + 82 + 252 + 12 + 22 + 62 + 22 + 92 + 52 + 92 + 32 + 82 + 852 + 82 + 32 + 92 + 92 = 8479.
by Yoshio Mimura, Kobe, Japan
8480
84802 = 85 + 125 + 205 + 245 + 365.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8481
84812 = 71927361, a zigzag square.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8484
84842 = 1083 + 2393 + 3853.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8485
84854 = 5183312422800625,
and 52 + 12 + 82 + 32 + 32 + 122 + 422 + 22 + 802 + 02 + 62 + 22 + 52 = 8485.
by Yoshio Mimura, Kobe, Japan
8486
84862 = 763 + 1293 + 4113.
84865 = 44006328579092142176 :
42 + 42 + 02 + 02 + 62 + 322 + 82 + 52 + 792 + 02 + 92 + 212 + 42 + 212 + 72 + 62
= 42 + 42 + 02 + 02 + 632 + 282 + 572 + 92 + 02 + 92 + 22 + 142 + 22 + 12 + 72 + 62 = 8486.
by Yoshio Mimura, Kobe, Japan
8487
84872 = 72029169, and 72 + 22 + 02 + 22 + 92 + 12 + 62 + 92 = 162.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8488
84884 = 5190646865268736,
and 52 + 12 + 92 + 02 + 642 + 62 + 82 + 62 + 522 + 62 + 82 + 72 + 362 = 8488.
by Yoshio Mimura, Kobe, Japan
8490
84902 = 13 + 2913 + 3623 = 393 + 2863 + 3653.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8493
84935 = 44188129736034525693 :
42 + 412 + 82 + 82 + 122 + 92 + 72 + 32 + 602 + 32 + 452 + 252 + 62 + 92 + 32 = 8493.
by Yoshio Mimura, Kobe, Japan
8494
84942 = 72148036, a square with different digits.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8495
84952 = 72165025, and 72 + 22 + 12 + 62 + 52 + 02 + 22 + 52 = 122.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8496
84962 = 403 + 3003 + 3563.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8497
84972 = 2123 + 2503 + 3613.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
8498
84985 = 44318355184220679968 :
42 + 42 + 32 + 182 + 32 + 552 + 182 + 42 + 22 + 22 + 02 + 672 + 92 + 92 + 62 + 82 = 8498.
by Yoshio Mimura, Kobe, Japan