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3400 - 3499

3400

34002 = (12 + 4)(62 + 4)(92 + 4)(262 + 4) = (92 + 4)(142 + 4)(262 + 4).

Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3401

34012 = 203 + 253 + 2263.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

3402

34022 = (12 + 5)(22 + 5)(42 + 5)(1012 + 5) = (22 + 5)(112 + 5)(1012 + 5) = (42 + 5)(72 + 5)(1012 + 5).

34022 = 293 + 1593 + 1963.

Komachi equation: 34022 = 92 * 872 * 62 - 542 * 32 * 22 * 102.

Page of Squares : First Upload August 10, 2008 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3403

3403 = (12 + 22 + 32 + ... + 822) / (12 + 22 + 32 + 42 + 52).

34032 = 1483 + 1523 + 1693.

34032 + 34042 + 34052 + ... + 34442 = 34452 + 34462 + 34472 + ... + 34852.

Page of Squares : First Upload August 10, 2008 ; Last Revised September 13, 2011
by Yoshio Mimura, Kobe, Japan

3405

34052 = 863 + 1053 + 2143 = 15 + 145 + 175 + 205 + 235.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

3406

34062 = 152 + 162 + 172 + 182 + 192 + 202 + ... + 3262.

Page of Squares : First Upload June 25, 2007 ; Last Revised June 25, 2007
by Yoshio Mimura, Kobe, Japan

3407

34072 = 203 + 1743 + 1853.

1 / 3407 = 0.00029351335485, 292 + 32 + 52 + 132 + 32 + 52 + 482 + 52 = 3407.

Page of Squares : First Upload June 25, 2007 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

3408

34082 = 11614464, a square with just 3 kinds of digits.

34082 = 1203 + 1483 + 1883.

The square root of 3408 is 58.37...., 58 = 32 + 72.

Page of Squares : First Upload June 25, 2007 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

3409

34092 = 11621281, 1 + 1 * 6 + 21 * 2 * 81 = 1 * 1 + 6 + 21 * 2 * 81 = 3409.

Page of Squares : First Upload June 25, 2007 ; Last Revised June 25, 2007
by Yoshio Mimura, Kobe, Japan

3410

34102 = (22 + 6)(52 + 6)(72 + 6)(262 + 6) = (42 + 6)(72 + 6)(982 + 6).

34102 = 833 + 1693 + 1843.

Page of Squares : First Upload August 10, 2008 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3411

34112 = 893 + 1713 + 1813 = 903 + 1663 + 1853 = 1113 + 1293 + 2013.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

3414

34142 = 11655396, 1 - 1 + 6 * 553 + 96 = 1 * 1 * 6 * 553 + 96 = 3414.

Page of Squares : First Upload June 25, 2007 ; Last Revised June 25, 2007
by Yoshio Mimura, Kobe, Japan

3416

A cubic polynomial :
(X + 1832)(X + 2882)(X + 34162) = X3 + 34332X2 + 11668082X + 1800368642.

The quadratic polynomial -3416X2 + 22624X - 10559 takes the values 932, 1452, 1632, 1592, 1312, 472 at X = 1, 2,..., 6,

Page of Squares : First Upload June 25, 2007 ; Last Revised December 15, 2008
by Yoshio Mimura, Kobe, Japan

3417

3417 = (12 + 22 + 32 + ... + 672) / (12 + 32 + 42).

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

3418

Loop of length 10 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
3418 - 1480 - 6596 - 13441 - ... - 4768 - 6833 - 5713 - 3418
(Note f(3418) = 342 + 182 = 1480,   f(1480) = 142 + 802 = 6596, etc. See 1268)

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

3420

Komachi equations:
34202 = 92 * 82 * 762 * 52 * 42 / 322 */ 12 = 92 / 82 * 762 * 52 / 42 * 322 */ 12.

Page of Squares : First Upload October 1, 2010 ; Last Revised October 1, 2010
by Yoshio Mimura, Kobe, Japan

3421

34212 = 11703241, 12 + 12 + 72 + 02 + 32 + 22 + 42 + 12 = 92.

Page of Squares : First Upload June 25, 2007 ; Last Revised June 25, 2007
by Yoshio Mimura, Kobe, Japan

3423

34232 = 13022 + 21422 + 23312 = 13322 + 24122 + 20312.

Page of Squares : First Upload September 18, 2013 ; Last Revised September 18, 2013
by Yoshio Mimura, Kobe, Japan

3424

34242 = (12 + 7)(102 + 7)(1172 + 7) = (102 + 7)(3312 + 7).

34242 = 443 + 1163 + 2163.

(34242 + 2) = (12 + 2)(32 + 2)(52 + 2)(72 + 2)(162 + 2).

Page of Squares : First Upload June 25, 2007 ; Last December 21, 2013
by Yoshio Mimura, Kobe, Japan

3425

34252 = 104 + 104 + 404 + 554.

Loop of length 5 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
3425 - 1781 - 6850 - 7124 - ... - 6850 - 7124 - 5617 - 3425
(Note f(3425)= 342 + 252 = 1781,   f(1781) = 172 + 812 = 6850, etc. See 1781)

Page of Squares : First Upload August 10, 2008 ; Last Revised October 9, 2008
by Yoshio Mimura, Kobe, Japan

3426

The square root of 3426 is 58.532042...., and 58 = 52 + 32 + 22 + 02 + 42 + 22.

Page of Squares : First Upload June 25, 2007 ; Last Revised June 25, 2007
by Yoshio Mimura, Kobe, Japan

3429

34292 = 1453 + 1563 + 1703.

1 / 3429 = 0.0002916...., and 2916 = 542.

Page of Squares : First Upload June 25, 2007 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

3430

Komachi equations:
34302 = 982 * 72 * 62 * 52 / 42 / 32 * 22 */ 12 = 982 * 72 / 62 * 52 * 42 * 32 / 22 */ 12.

34302 = (4 + 5 + 6 + 7 + 8 + 9 + 10)2 + (11 + 12 + 13 + 14 + 15 + 16 + 17)2 + (18 + 19 + 20 + 21 + 22 + 23 + 24)2 + ... + (165 + 166 + 167 + 168 + 169 + 170 + 171)2.

938k + 1274k + 3430k + 6902k are squares for k = 1,2,3 (1122, 78682, 6099522).

Page of Squares : First Upload June 25, 2007 ; Last Revised June 3, 2011
by Yoshio Mimura, Kobe, Japan

3431

34312 = 11771761, a square with just 3 kinds of digits.

Page of Squares : First Upload June 25, 2007 ; Last Revised June 25, 2007
by Yoshio Mimura, Kobe, Japan

3432

34322± 5 are primes.

34322 = (122 - 1)(2872 - 1).

Page of Squares : First Upload December 21, 2013 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

3433

34332 = 14 + 284 + 344 + 564 = 144 + 144 + 374 + 564.

A cubic polynomial :
(X + 1832)(X + 2882)(X + 34162) = X3 + 34332X2 + 11668082X + 1800368642.

Page of Squares : First Upload June 25, 2007 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

3437

34372 = S2(182) + S2(308), where S2(n) = 12 + 22 + 32 + 42 + .... + n2.

34372 = 11812969, 118 * 1 * 29 + 6 + 9 = 3437.

294k + 1288k + 1617k + 2730k are squares for k = 1,2,3 (772, 34372, 1635132).

Page of Squares : First Upload June 25, 2007 ; Last Revised June 3, 2011
by Yoshio Mimura, Kobe, Japan

3441

34412 = 11840481, 1 - 1 + 840 * 4 + 81 = 1 * 1 * 840 * 4 + 81 = 3441.

3441k + 6290k + 10138k + 14356k are squares for k = 1,2,3 (1852, 189812, 20712972).

Page of Squares : First Upload June 25, 2007 ; Last Revised June 3, 2011
by Yoshio Mimura, Kobe, Japan

3444

34442± 5 are primes.

34442 = 143 + 1603 + 1983.

Page of Squares : First Upload August 10, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

3445

3445 = (12 + 22 + 32 + ... + 522) / (12 + 22 + 32).

34452 = 11868025, 1 - 1 + 86 * 80 / 2 + 5 = 1 * 1 * 86 * 80 / 2 + 5 = 3445.

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

3446

34462 = 11874916, 11 - 8 + 7 * 491 + 6 = 3446.

Page of Squares : First Upload June 25, 2007 ; Last Revised June 25, 2007
by Yoshio Mimura, Kobe, Japan

3447

34472 = 493 + 993 + 2213.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

3449

1 / N = 0.000289...., and 289 = 172 (N = 3449,..., 3460).

Page of Squares : First Upload June 25, 2007 ; Last Revised June 25, 2007
by Yoshio Mimura, Kobe, Japan

3450

The square root of 3450 is 58.73...., and 58 = 72 + 32.

S2(3450) = S2(2669) + S2(2804), where S2(n) = 12 + 22 + 32 + 42 + .... + n2.

34502 = (83 + 84 + 85 + 86 + 87)2 + (88 + 89 + 90 + 91 + 92)2 + (93 + 94 + 95 + 96 + 97)2 + ... + (193 + 194 + 195 + 196 + 197)2.

3450k + 10833k + 12972k + 15594k are squares for k = 1,2,3 (2072, 232532, 26994872).

Page of Squares : First Upload June 25, 2007 ; Last Revised June 3, 2011
by Yoshio Mimura, Kobe, Japan

3451

11102 + 34512 = 13141501, a mosaic square.

Page of Squares : First Upload June 25, 2007 ; Last Revised June 25, 2007
by Yoshio Mimura, Kobe, Japan

3453

34532± 2 are primes.

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

3454

34542 = 11930116, 119 * 30 - 116 = 1 - 1 * 9 + 577 * 6 + 4 = 1 * 1 - 9 + 577 * 6 + 4
    = 11 + 9 * 64 * 6 - 8 * 1 = 3459.

Page of Squares : First Upload June 25, 2007 ; Last Revised June 25, 2007
by Yoshio Mimura, Kobe, Japan

3456

34562 = 126 + 126 + 126 + 126.

602 + 3456 = 842, 602 - 3456 = 122.

Komachi equations:
34562 = 12 / 22 * 32 * 42 * 562 / 72 * 82 * 92 = 92 * 82 / 72 * 62 / 52 * 42 / 32 * 2102.

Page of Squares : First Upload August 10, 2008 ; Last Revised July 27, 2011
by Yoshio Mimura, Kobe, Japan

3458

34582 = (22 + 3)(13072 + 3) = (42 + 3)(72 + 3)(1102 + 3).

Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3459

34592 = 1103 + 1723 + 1773.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

3460

Loop of length 4 (See 41):
3460 -- 342 + 602 = 4756 -- 472 + 562 = 5345 -- 532 + 452 = 4834 -- 482 + 342 = 3460

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

3462

34622 = (12 + 2)(22 + 2)(8162 + 2) = (42 + 2)(8162 + 2).

Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3463

34632 = 244 + 244 + 414 + 544.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

3465

34652 = (83 + 84 + 85)2 + (86 + 87 + 88)2 + (89 + 90 + 91)2 + ... + (230 + 231 + 232)2.

34652 = 912 + 922 + 932 + 942 + 952 + 962 + ... + 3322.

34652 = (22 - 1)(62 - 1)(102 - 1)(342 - 1).

18k + 84k + 129k + 210k are squares for k = 1,2,3 (212, 2612, 34652).

Page of Squares : First Upload June 25, 2007 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3468

34682 = 73 + 863 + 2253.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

3472

34722 = 12054784 appears in the decimal expressions of π:
  π = 3.14159•••12054784••• (from the 27922nd digit)
  (12054784 is the third 8-digit square in the expression of π.)

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

3473

34732 = 12061729, a zigzag square.

34732 = 44 + 194 + 284 + 584.

34732 = 12061729, 1 * 206 * 17 - 29 = 3473.

34734 = 145485306469441, and 12 + 42 + 52 + 482 + 52 + 302 + 62 + 42 + 62 + 92 + 42 + 42 + 12 = 3473.

Page of Squares : First Upload June 25, 2007 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

3474

34745 = 505998314925198624 : 52 + 02 + 52 + 92 + 92 + 82 + 32 + 12 + 492 + 22 + 52 + 12 + 92 + 82 + 62 + 242 = 3474.

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

3475

34752 = 12075625, a zigzag square.

34752 = 12075625, 12 + 22 + 02 + 72 + 52 + 62 + 22 + 52 = 122.

Page of Squares : First Upload June 25, 2007 ; Last Revised June 25, 2007
by Yoshio Mimura, Kobe, Japan

3476

34762 = (132 + 7)(2622 + 7) = (22 + 7)(32 + 7)(2622 + 7).

Page of Squares : First Upload December 21, 2013 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3481

The square of 59.

Page of Squares : First Upload June 25, 2007 ; Last Revised June 25, 2007
by Yoshio Mimura, Kobe, Japan

3482

34822 = 12124324, a square every digit of which is non-zero and smaller than 5.

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

3484

34842 = 133 + 763 + 2273.

34842 = 12138256, 12 + 22 + 12 + 32 + 82 + 22 + 52 + 62 = 122.

34842 = (72 + 3)(82 + 3)(592 + 3).

Page of Squares : First Upload June 25, 2007 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3485

34852 = (16 + 17 + 18 + ... + 56)2 + (57 + 58 + 59 + ... + 97)2 + (98 + 99 + 100 + ... + 138)2 + ... + (57 + 58 + 59 + ... + 97)2.

34852 = (22 + 1)(42 + 1)(3782 + 1).

Page of Squares : First Upload June 25, 2007 ; Last Revised November 2, 2013
by Yoshio Mimura, Kobe, Japan

3486

34862 = (12 + 5)(242 + 5)(592 + 5).

34862 = 203 + 913 + 2253.

Page of Squares : First Upload August 10, 2008 ; Last Revised December 21, 2013
by Yoshio Mimura, Kobe, Japan

3489

34892 = 633 + 1493 + 2053.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

3492

34922 = 43 + 303 + 2303 = 244 + 364 + 364 + 544.

34925 = 519243627351647232 : 52 + 192 + 22 + 432 + 62 + 22 + 72 + 32 + 52 + 12 + 62 + 42 + 72 + 22 + 322 = 3492.

Page of Squares : First Upload August 10, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

3493

34932 = 713 + 913 + 2233.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan

3495

34952 = 12215025, 12 + 22 + 22 + 12 + 52 + 02 + 22 + 52 = 82.

Page of Squares : First Upload June 25, 2007 ; Last Revised June 25, 2007
by Yoshio Mimura, Kobe, Japan

3497

2080k + 3497k + 4004k + 4108k are squares for k = 1,2,3 (1172, 70332, 4304432).

Page of Squares : First Upload June 3, 2011 ; Last Revised June 3, 2011
by Yoshio Mimura, Kobe, Japan

3498

34982 = 94 + 134 + 174 + 594.

Page of Squares : First Upload August 10, 2008 ; Last Revised August 10, 2008
by Yoshio Mimura, Kobe, Japan