7400
74002 = (12 + 4)(142 + 4)(2342 + 4) = (22 + 4)(112 + 4)(2342 + 4) = (42 + 4)(122 + 4)(1362 + 4).
Page of Squares : First Upload January 11, 2014 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7402
74022± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
7403
74032 = 1193 + 1653 + 3653.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7405
74055 = 22265134054473128125 :
22 + 22 + 22 + 62 + 52 + 12 + 32 + 42 + 02 + 52 + 42 + 42 + 72 + 32 + 12 + 22 + 812 + 252 = 7405.
by Yoshio Mimura, Kobe, Japan
7406
74064 = 3008394810554896,
and 32 + 02 + 02 + 832 + 92 + 42 + 82 + 102 + 52 + 52 + 42 + 82 + 92 + 62 = 7406.
by Yoshio Mimura, Kobe, Japan
7407
74072 = 1353 + 2953 + 2993,
74072 = 234 + 324 + 444 + 844.
Komachi equations:
74072 = 98762 * 52 / 42 * 32 * 22 / 102 = 98762 / 52 / 42 * 32 / 22 * 102.
1 / 7407 = 0.000135007425408, 12 + 352 + 02 + 02 + 742 + 252 + 42 + 082 = 7407,
1 / 7407 = 0.000135007425408, 12 + 352 + 02 + 0742 + 252 + 42 + 02 + 82 = 7407,
1 / 7407 = 0.000135007425408, 12 + 352 + 02 + 0742 + 252 + 42 + 082 = 7407,
1 / 7407 = 0.000135007425408, 12 + 352 + 002 + 742 + 252 + 42 + 02 + 82 = 7407,
1 / 7407 = 0.000135007425408, 12 + 352 + 002 + 742 + 252 + 42 + 082 = 7407,
1 / 7407 = 0.000135007425408, 12 + 352 + 00742 + 252 + 42 + 02 + 82 = 7407,
1 / 7407 = 0.000135007425408, 12 + 352 + 00742 + 252 + 42 + 082 = 7407.
by Yoshio Mimura, Kobe, Japan
7408
74082 = 54878464, a zigzag square.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7409
74095 = 22325334462883216049 :
22 + 22 + 32 + 22 + 52 + 332 + 442 + 622 + 82 + 82 + 32 + 22 + 162 + 02 + 42 + 92 = 7409,
22 + 232 + 252 + 332 + 42 + 42 + 622 + 82 + 82 + 322 + 12 + 62 + 02 + 42 + 92 = 7409.
by Yoshio Mimura, Kobe, Japan
7412
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
7412 - 5620 - 3536 - 2521 - ... - 2874 - 6260 - 7444 - 7412
(Note f(7412) = 742 + 122 = 5620, f(5620) = 562 + 202 = 3536, etc. See 41)
by Yoshio Mimura, Kobe, Japan
7414
74142 = 54967396, a zigzag square.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7415
74152 = 54982225, and 5 * 4 + 9 * 822 + 2 - 5 = 7415.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7419
74195 = 22476405331452753099 :
22 + 22 + 472 + 62 + 42 + 02 + 52 + 332 + 142 + 522 + 72 + 52 + 302 + 92 + 92 = 7419.
by Yoshio Mimura, Kobe, Japan
7421
The square root of 7421 is 86.145226...., and 86 = 12 + 42 + 52 + 22 + 22 + 62.
74212 = 55071241, and 52 + 52 + 02 + 72 + 12 + 22 + 42 + 12 = 112.
Loop of length 5 : 7421 --- 742 + 212 = 5917 --- 592 + 172 = 3770 -- 372 + 702 = 6269 --- 622 + 692 = 8605 --- 862 + 052 = 7421
Page of Squares : First Upload April 30, 2008 ; Last Revised October 9, 2008by Yoshio Mimura, Kobe, Japan
7422
The square root of 7422 is 86.15103017...., and 86 = 12 + 52 + 12 + 02 + 32 + 02 + 12 + 72.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7424
74242 = 55115776, a square with odd digits except the last digit 6.
74242 = (12 + 7)(32 + 7)(152 + 7)(432 + 7) = (112 + 7)(152 + 7)(432 + 7).
The square root of 7424 is 86.16263...., and 86 = 12 + 62 + 22 + 62 + 32.
74242 = 643 + 2243 + 3523.
Page of Squares : First Upload April 30, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7426
The square root of 7426 is 86.17424...., and 86 = 12 + 72 + 42 + 22 + 42.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7432
74322 = 144 + 144 + 264 + 864.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7435
74352 = 1563 + 1693 + 3603.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7438
12 + 22 + 32 + 42 + ... + 74382 = 137193913719 is the first 12-digit sum consisting of odd digits (there are such two 12-digit sums, see 12149).
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7440
74402 = (42 - 1)(19212 - 1).
74402 = 443 + 2923 + 3123.
Page of Squares : First Upload April 30, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7441
74415 = 22811640709248613201 :
22 + 22 + 82 + 12 + 162 + 402 + 702 + 92 + 22 + 42 + 82 + 62 + 12 + 32 + 202 + 12 = 7441.
by Yoshio Mimura, Kobe, Japan
7442
74422 = 613 + 1833 + 3663,
74422 = 614 + 614 + 614 + 614.
74425 = 22826973173212243232 :
22 + 22 + 82 + 22 + 62 + 92 + 732 + 172 + 32 + 22 + 12 + 22 + 242 + 32 + 22 + 322
= 22 + 22 + 82 + 22 + 62 + 92 + 732 + 172 + 32 + 22 + 12 + 22 + 242 + 322 + 32 + 22
= 22 + 22 + 82 + 22 + 62 + 92 + 732 + 172 + 322 + 12 + 22 + 242 + 32 + 22 + 32 + 22
= 22 + 282 + 22 + 62 + 92 + 72 + 312 + 732 + 22 + 122 + 22 + 42 + 32 + 22 + 32 + 22 = 7442.
by Yoshio Mimura, Kobe, Japan
7443
74432 = 55398249, and 5 - 5 + 3 * 9 + 824 * 9 = 5 / 5 * 3 * 9 + 824 * 9 = 7443.
74432 = 1183 + 1523 + 3693.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7444
74442 = 55413136, and 5 + 5 + 413 * 1 * 3 * 6 = 7444.
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
7444 - 7412 - 5620 - 3536 - ... - 10853 - 2874 - 6260 - 7444
(Note f(7444) = 742 + 442 = 7412, f(7412) = 742 + 122 = 5620, etc. See 41)
by Yoshio Mimura, Kobe, Japan
7445
74455 = 22873020037957653125 :
22 + 22 + 82 + 72 + 302 + 202 + 02 + 32 + 72 + 92 + 52 + 72 + 652 + 312 + 252 = 7445.
by Yoshio Mimura, Kobe, Japan
7446
74462 = (102 + 2)(122 + 2)(612 + 2).
3366k + 7446k + 15708k + 38505k are squares for k = 1,2,3 (2552, 423812, 78368132).
Page of Squares : First Upload July 8, 2011 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7447
74472 = 443 + 3003 + 3053.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7448
74482 = (12 + 3)(22 + 3)(232 + 3)(612 + 3) = (12 + 3)(22 + 3)(42 + 3)(52 + 3)(612 + 3)
= (12 + 3)(42 + 3)(232 + 3)(372 + 3) = (52 + 3)(232 + 3)(612 + 3).
74482 = 203 + 843 + 3803 = 2243 + 2663 + 2943.
Page of Squares : First Upload April 30, 2008 ; Last Revised January 11, 2014by Yoshio Mimura, Kobe, Japan
7449
74492 = 2013 + 2603 + 3103.
74495 = 22934531418412512249 :
22 + 292 + 32 + 452 + 312 + 42 + 12 + 82 + 42 + 12 + 252 + 12 + 222 + 492 = 7449.
by Yoshio Mimura, Kobe, Japan
7450
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
7450 - 7976 - 12017 - 690 - ... 4441 - 3617 - 1585 - 7450
(Note f(7450) = 742 + 502 = 7976, f(7976) = 792 + 762 = 12017, etc. See 41)
by Yoshio Mimura, Kobe, Japan
7451
74512 = 55517401, 55 - 5 + 1 * 7401 = 55 - 5 * 1 + 7401 = 7451.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7452
74522 = (59 + 60 + 61 + 62 + 63 + 64 + 65 + 66 + 67)2 + (68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76)2 + (77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85)2 + ... + (257 + 258 + 259 + 260 + 261 + 262 + 263 + 264 + 265)2.
74522 = 184 + 244 + 484 + 844 = 184 + 364 + 724 + 724 = 244 + 264 + 684 + 764.
74525 = 22980751740810796032 :
22 + 292 + 82 + 02 + 72 + 52 + 12 + 72 + 402 + 82 + 12 + 02 + 72 + 92 + 602 + 322 = 7452.
by Yoshio Mimura, Kobe, Japan
7453
74532 = 55547209, and 52 + 52 + 52 + 42 + 72 + 22 + 02 + 92 = 152.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7455
74555 = 23027046552026409375 :
232 + 02 + 272 + 02 + 42 + 652 + 52 + 202 + 22 + 62 + 42 + 02 + 92 + 372 + 52 = 7455.
by Yoshio Mimura, Kobe, Japan
7456
74562 = 55591936, a square with odd digits except the last digit 6.
Page of Squares : First Upload August 24, 2013 ; Last Revised August 24, 2013by Yoshio Mimura, Kobe, Japan
7458
74582 = 1473 + 2423 + 3373,
74582 = 34 + 414 + 614 + 794.
by Yoshio Mimura, Kobe, Japan
7462
74622± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
7463
74632 = 2872 + 2882 + 2892 + 2902 + 2912 + ... + 5752.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7466
74662 = 55741156, 5 * 5 + 7411 + 5 * 6 = 7466.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7468
74682 = 55771024, and 52 + 52 + 72 + 72 + 12 + 02 + 22 + 42 = 132.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7469
517k + 869k + 3245k + 7469k are squares for k = 1,2,3 (1102, 82062, 6720342).
Page of Squares : First Upload July 8, 2011 ; Last Revised July 8, 2011by Yoshio Mimura, Kobe, Japan
7471
74712 = 13 - 22 + 33 - 43 + 53 - 63 + 73 - 83 + ... + 4813.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7472
74722 = (94 + 95 + 96 + 97)2 + (98 + 99 + 100 + 101)2 + (102 + 103 + 104 + 105)2 + ... + (346 + 347 + 348 + 349)2.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7473
74732 = 55845729, and 52 + 52 + 82 + 42 + 52 + 72 + 22 + 92 = 172.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7475
74752 = 653 + 903 + 3803.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7476
74762 = 55890576, 5 - 5 + 890 / 5 * 7 * 6 = 5 / 5 * 890 / 5 * 7 * 6 = 7476.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7479
1 / 7479 = 0.000133707714935, 132 + 32 + 72 + 0772 + 12 + 42 + 92 + 352 = 7479.
The square root of 7479 is 86.48121...., and 86 = 42 + 82 + 12 + 22 + 12.
74795 = 23400097454226453399 :
232 + 42 + 02 + 02 + 02 + 92 + 742 + 52 + 42 + 22 + 22 + 62 + 42 + 52 + 332 + 92 + 92 = 7479.
by Yoshio Mimura, Kobe, Japan
7480
74802 = 1093 + 1473 + 3723.
74805 = 23415745505996800000 :
22 + 32 + 412 + 52 + 72 + 452 + 52 + 02 + 592 + 92 + 62 + 82 + 02 + 02 + 02 + 02 + 02 = 7480.
by Yoshio Mimura, Kobe, Japan
7481
74812 = 155 + 235 + 275 + 285 + 285.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7482
74822 = 1493 + 2953 + 3003.
74824 = 3133796675144976,
and 32 + 12 + 32 + 32 + 72 + 92 + 62 + 672 + 512 + 42 + 42 + 92 + 72 + 62 = 7482.
74825 = 23447066723434710432 :
22 + 32 + 442 + 72 + 02 + 62 + 62 + 722 + 32 + 42 + 32 + 42 + 72 + 102 + 42 + 32 + 22 = 7482.
by Yoshio Mimura, Kobe, Japan
7483
74835 = 23462739895818117643 :
22 + 342 + 622 + 72 + 392 + 82 + 92 + 52 + 82 + 182 + 12 + 172 + 62 + 42 + 32 = 7483.
by Yoshio Mimura, Kobe, Japan
7484
74842 = 1623 + 2363 + 3383.
74845 = 23478421448456551424 :
22 + 32 + 42 + 72 + 82 + 422 + 142 + 42 + 82 + 452 + 62 + 552 + 142 + 22 + 42 = 7484.
by Yoshio Mimura, Kobe, Japan
7487
74875 = 23525516421508166207 :
22 + 352 + 252 + 52 + 162 + 42 + 212 + 52 + 02 + 82 + 12 + 662 + 202 + 72 = 7487.
by Yoshio Mimura, Kobe, Japan
7490
74902= 434 x 435 + 435 x 436 + 436 x 437 + 437 x 438 + ... + 629 x 630.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7492
The square root of 7492 is 86.556...., and 86 = 52 + 52 + 62.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7493
74934 = 3152266527212401,
and 312 + 52 + 22 + 262 + 62 + 52 + 22 + 722 + 12 + 242 + 02 + 12 = 7493.
by Yoshio Mimura, Kobe, Japan
7494
74942 = 153 + 1963 + 3653.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7495
74952 = 56175025, and 5 - 6 - 1 + 7502 - 5 = 7495.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7496
74962 = 363 + 1443 + 3763.
Page of Squares : First Upload April 30, 2008 ; Last Revised April 30, 2008by Yoshio Mimura, Kobe, Japan
7497
Komachi equation: 74972 = 12 / 22 * 342 * 562 * 72 / 82 * 92.
74972 is written as the sum of four fourths in four ways :
74972 = 124 + 214 + 664 + 784 = 124 + 264 + 644 + 794 = 144 + 284 + 494 + 844 = 214 + 424 + 424 + 844.
74972 = 253 + 263 + 273 + 283 + 293 + 303 + ... + 1223.
Page of Squares : First Upload April 30, 2008 ; Last Revised November 5, 2010by Yoshio Mimura, Kobe, Japan
7498
7498k + 13662k + 15778k + 15962k are squares for k = 1,2,3 (2302, 273242, 33115402).
Page of Squares : First Upload July 8, 2011 ; Last Revised July 8, 2011by Yoshio Mimura, Kobe, Japan
7499
74992 = 56235001, and 52 + 62 + 22 + 32 + 52 + 02 + 02 + 12 = 102.
74994 = 3162375337470001,
and 32 + 12 + 62 + 22 + 372 + 52 + 332 + 72 + 42 + 702 + 02 + 02 + 12 = 7499.
by Yoshio Mimura, Kobe, Japan