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4700 - 4799

4702

47022 = 12 + 172 + 372 + 672

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

4703

47032 = 22 + 232 + 262 + 682

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

4704

47042 = 562 + 2802

A cubic polynomial :
(X + 652)(X + 722)(X + 47042) = X3 + 47052X2 + 4563122X + 220147202.

702 + 4704 = 982, 702 - 4704 = 142.

Komachi equations:
47042 = 12 * 22 / 32 / 42 * 562 * 72 * 82 * 92 = 92 * 82 * 72 / 62 / 52 * 42 / 32 * 2102
 = 982 / 72 * 62 / 52 * 42 / 32 * 2102.

Page of Squares : First Upload October 1, 2007 ; Last Revised August 2, 2011
by Yoshio Mimura, Kobe, Japan

4705

A cubic polynomials :
(X + 652)(X + 722)(X + 47042) = X3 + 47052X2 + 4563122X + 220147202,
(X + 5602)(X + 18632)(X + 42842) = X3 + 47052X2 + 83989082X + 44694115202.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 1, 2007
by Yoshio Mimura, Kobe, Japan

4707

47072 = 442 + 2172 + 2282

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

4709

47092 = 22174681, 2 * 2 * 1 * 7 + 4681 = 22 - 1 + 7 + 4681 = 4709.

47094 = 491716477451761,
and 42 + 92 + 12 + 72 + 12 + 642 + 72 + 72 + 42 + 52 + 172 + 62 + 12 = 4709,
47094 = 491716477451761,
and 42 + 92 + 172 + 12 + 642 + 72 + 72 + 42 + 52 + 12 + 72 + 62 + 12 = 4709.

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

4710

47102 = 782 + 972 + 2752

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

4712

47122 = 602 + 1642 + 2602 = 382 + 422 + 542 + 542

The square root of 4712 is 68.644..., and 68 = 62 + 42 + 42.

Page of Squares : First Upload October 1, 2007 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan

4715

47152 = 1162 + 1932 + 2382

47152 = (122 + 123 + 124 + ... + 144)2 + (145 + 146 + 147 + ... + 167)2 + (168 + 169 + 170 + ... + 190)2 + ... + (145 + 146 + 147 + ... + 167)2.

Page of Squares : First Upload October 1, 2007 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan

4721

47212 = 252 + 402 + 402 + 642.

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

4724

47242 = 302 + 1982 + 2442 = 502 + 2202 + 2262

1 / 4724 = 0.0002116... and 2116 = 462. (also 4725).

The square root of 4724 is 68.7313..., and 68 = 72 + 32 + 12 + 32.

Page of Squares : First Upload October 1, 2007 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan

4725

47252 = (42 - 1)(62 - 1)(82 - 1)(262 - 1).

Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4728

47282 = 772 + 1422 + 2672

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

4732

47322 = (12 + 3)(192 + 3)(1242 + 3) = (12 + 3)(22 + 3)(72 + 3)(1242 + 3)
= (52 + 3)(72 + 3)(1242 + 3).

47322 = 262 + 522 + 522 + 522

Page of Squares : First Upload September 4, 2008 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4733

47332 = 1052 + 1982 + 2382

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

4734

12 + 22 + 32 + 42 + 52 + 62 + ... + 47342 = 35375379135, the first 11-digit sum whose digits are odd (there are 3 such sums in all. See 5382, 6102).

Page of Squares : First Upload October 1, 2007 ; Last Revised October 1, 2007
by Yoshio Mimura, Kobe, Japan

4735

47352 = 1402 + 1932 + 2322

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

4737

The square root of 4737 is 68.82..., and 68 = 82 + 22.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 1, 2007
by Yoshio Mimura, Kobe, Japan

4738

47382 = 22448644, a square with even digits.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 1, 2007
by Yoshio Mimura, Kobe, Japan

4742

47422± 3 are primes.

47422 = 72 + 1412 + 2702.

Page of Squares : First Upload September 4, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

4743

47432 = 62 + 412 + 562 + 562

47432 = 22496049, and 22 * 4 * 9 * 6 + 0 * 4 - 9 = 4743.

Page of Squares : First Upload October 1, 2007 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan

4744

47442 = 402 + 1742 + 2582.

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

4745

47452 = (22 + 9)(82 + 9)(1542 + 9).

Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4746

47462 = 92 + 832 + 2802.

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

4747

1 / 4747 = 0.000210659, 212 + 02 + 652 + 92 = 4747,
1 / 4747 = 0.000210659, 212 + 0652 + 92 = 4747.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 1, 2007
by Yoshio Mimura, Kobe, Japan

4750

47502 = 22562500, and 225 = 152, 62500 = 2502.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 1, 2007
by Yoshio Mimura, Kobe, Japan

4752

47522± 5 are primes.

47522 = (12 + 8)(22 + 8)(162 + 8)(282 + 8) = (12 + 8)(22 + 8)(42 + 8)(52 + 8)(162 + 8)
= (12 + 8)(42 + 8)(52 + 8)(62 + 8)(82 + 8) = (12 + 8)(42 + 8)(82 + 8)(382 + 8)
= (12 + 8)(62 + 8)(82 + 8)(282 + 8) = (102 + 8)(162 + 8)(282 + 8)
= (22 + 8)(42 + 8)(162 + 8)(172 + 8) = (22 + 8)(42 + 8)(2802 + 8) = (22 + 8)(52 + 8)(82 + 8)(282 + 8) = (42 + 8)(52 + 8)(102 + 8)(162 + 8) = (42 + 8)(62 + 8)(82 + 8)(172 + 8) = (62 + 8)(162 + 8)(442 + 8).

47522 = 192 + 532 + 2822 = 1082 + 1862 + 2462 = 1112 + 1692 + 2542

47522 = 22581504 appears in the decimal expressions of e:
  e = 2.71828•••22581504••• (from the 29097th digit)
  (22581504 is the fifth 8-digit square in the expression of e.)

Page of Squares : First Upload September 4, 2008 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

4753

47532 = 492 + 1542 + 2662 = 12 + 342 + 462 + 642 = 282 + 422 + 422 + 632

47532 = 22591009, and 22 + 22 + 52 + 92 + 12 + 02 + 02 + 92 = 142.

Page of Squares : First Upload October 1, 2007 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan

4756

47562± 3 are primes.

47562 = 22619536, and 22 + 22 + 62 + 12 + 92 + 52 + 32 + 62 = 142.

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

Page of Squares : First Upload October 1, 2007 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

4759

47592 = 202 + 202 + 462 + 652

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

4760

47602= 431 x 432 + 432 x 433 + 433 x 434 + 434 x 435 + ... + 528 x 529.

Komachi equation: 47602 = 982 * 7652 * 42 / 32 / 212.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 15, 2010
by Yoshio Mimura, Kobe, Japan

4761

The square of 69.

47612 = 842 + 1202 + 2732

Page of Squares : First Upload October 1, 2007 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan

4762

The square root of 4762 is 69.00724..., and 69 = 02 + 02 + 72 + 22 + 42.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 1, 2007
by Yoshio Mimura, Kobe, Japan

4763

47635 = 2451336362939320043 : 22 + 452 + 132 + 32 + 62 + 362 + 22 + 92 + 32 + 92 + 322 + 02 + 02 + 42 + 32 = 22 + 452 + 132 + 362 + 32 + 62 + 22 + 92 + 32 + 92 + 322 + 02 + 02 + 42 + 32 = 4763.

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

4765

A cubic polynomial :
(X + 322)(X + 22052)(X + 42242) = X3 + 47652X2 + 93151682X + 2980454402.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 1, 2007
by Yoshio Mimura, Kobe, Japan

4766

47662 = 22714756, and 2 + 2 + 7 - 1 + 4756 = 2 * 2 + 7 - 1 + 4756 = 4766.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 1, 2007
by Yoshio Mimura, Kobe, Japan

4767

47672 = 22 + 92 + 342 + 682

47672 = (150 + 151 + 152)2 + (153 + 154 + 155)2 + ... + (294 + 295 + 296)2.

Page of Squares : First Upload October 1, 2007 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan

4768

Loop of length 10 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
4768 - 6833 - 5713 - 3418 - ... - 2838 - 2228 - 1268 - 4768
(Note f(4768) = 472 + 682 = 6833,   f(6833) = 682 + 332 = 5713, etc. See 1268)

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

4770

47702 = (32 + 9)(162 + 9)(692 + 9).

Page of Squares : First Upload December 28, 2013 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4771

The square root of 4771 is 69.0724..., and 69 = 02 + 72 + 22 + 42.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 1, 2007
by Yoshio Mimura, Kobe, Japan

4772

47725 = 2474583854273733632 : 22 + 42 + 72 + 452 + 82 + 32 + 82 + 52 + 42 + 22 + 72 + 372 + 32 + 32 + 62 + 322 = 22 + 42 + 72 + 42 + 52 + 82 + 32 + 82 + 52 + 422 + 72 + 372 + 32 + 362 + 32 + 22 = 4772.

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

4775

47752 = 22800625, 2 - 2 + 800 * 6 - 25 = 2 / 2 * 800 * 6 - 25 = 4775.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 1, 2007
by Yoshio Mimura, Kobe, Japan

4776

47762 = 682 + 1602 + 2642

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

4779

47792 = (113 + 114 + 115)2 + (116 + 117 + 118)2 + (119 + 120 + 121)2 + ... + (287 + 288 + 289)2.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 1, 2007
by Yoshio Mimura, Kobe, Japan

4780

47802 = 102 + 2182 + 2322

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

4782

47825 = 2500620912904734432 : 22 + 52 + 02 + 02 + 62 + 202 + 92 + 12 + 292 + 02 + 472 + 342 + 42 + 32 + 22 = 4782.

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

4783

47832 = 22 + 182 + 182 + 692

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

4784

47845 = 2505854525373415424 : 22 + 52 + 02 + 52 + 82 + 52 + 452 + 22 + 52 + 372 + 342 + 12 + 52 + 42 + 22 + 42 = 4784.

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

4785

47852 = (92 + 6)(5132 + 6).

47854 = 524237119250625, and 52 + 22 + 42 + 22 + 372 + 112 + 92 + 22 + 502 + 62 + 252 = 4785.

4785k + 12265k + 14355k + 16995k are squares for k = 1,2,3 (2202, 258502, 31339002).

Page of Squares : First Upload December 1, 2008 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

4788

47882 = 722 + 1732 + 2592

47882 = 22924944, a square consisting of just 3 kinds of digits.

Komachi equation: 47882 = 92 / 82 * 762 / 52 * 42 / 32 * 2102.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 15, 2010
by Yoshio Mimura, Kobe, Japan

4789

47892 = 582 + 822 + 2812

47892 = 22934521, and 22 + 22 + 92 + 32 + 42 + 52 + 22 + 12 = 122.

Page of Squares : First Upload October 1, 2007 ; Last Revised September 4, 2008
by Yoshio Mimura, Kobe, Japan

4795

192 + 432 + 672 + 912 + 1152 + ... + (24n + 19)2 + ... + 11712 = 47952.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 1, 2007
by Yoshio Mimura, Kobe, Japan

4796

47962± 3 are primes.

47962 = 272 + 1202 + 2772

S2(4796) = S2(3531) + S2(4047), where S2(n) = 12 + 22 + 32 + ... + n2.

47962 = 23001616, and 2 + 300 * 16 - 1 * 6 = 2 + 300 * 16 * 1 - 6 = 4796.

Page of Squares : First Upload October 1, 2007 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

4797

47972 = 23011209, and 22 + 32 + 02 + 12 + 12 + 22 + 02 + 92 = 102.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 1, 2007
by Yoshio Mimura, Kobe, Japan

4798

47982 = 23020804, a zigzag square.

47982 = 23020804, and 2 + 30 * 20 * 8 + 0 - 4 = 4798.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 1, 2007
by Yoshio Mimura, Kobe, Japan

4799

47992 = 23030401, a zigzag square.

The square root of 4799 is 69.274..., and 69 = 22 + 72 + 42.

Page of Squares : First Upload October 1, 2007 ; Last Revised October 1, 2007
by Yoshio Mimura, Kobe, Japan