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970 - 979

970

The smallest squares containing k 970's :
297025 = 5452,
79707970276 = 2823262,
97097019703524 = 98537822.

(653 / 970)2 = 0.453192687... (Komachic).

Page of Squares : First Upload October 16, 2006 ; Last Revised October 16, 2006
by Yoshio Mimura, Kobe, Japan

971

The smallest squares containing k 971's :
119716 = 3462,
139719711681 = 3737912,
979711659719716 = 313003462.

(492 / 971)2 = 0.256738941... (Komachic),
(589 / 971)2 = 0.367952814... (Komachic).

82k + 298k + 628k + 673k are squares for k = 1,2,3 (412, 9712, 240732).

3-by-3 magic squares consisting of different squares with constant 9712:

A2B2C2
D2E2F2
G2H2K2
where (A, B, C, D, E, F, G, H, K) = 
(6, 423, 874, 631, 666, 318, 738, 566, 279)(9, 98, 966, 658, 711, 66, 714, 654, 73),
(9, 406, 882, 462, 774, 361, 854, 423, 186)(39, 314, 918, 678, 666, 199, 694, 633, 246),
(39, 546, 802, 678, 494, 489, 694, 633, 246)(46, 231, 942, 354, 882, 199, 903, 334, 126),
(46, 510, 825, 615, 654, 370, 750, 505, 354)(57, 494, 834, 594, 678, 361, 766, 489, 342),
(66, 246, 937, 519, 802, 174, 818, 489, 186)(66, 343, 906, 602, 726, 231, 759, 546, 262),
(71, 342, 906, 582, 711, 314, 774, 566, 153)(105, 450, 854, 654, 665, 270, 710, 546, 375),
(138, 441, 854, 546, 746, 297, 791, 438, 354)(183, 594, 746, 654, 631, 342, 694, 438, 519),
(186, 521, 798, 567, 714, 334, 766, 402, 441) 

9712 = 942841, 9 + 4 + 2 + 8 + 41 = 82,
9712 = 942841, 9 + 4 + 2 + 84 + 1 = 102,
9712 = 942841, 9 + 42 + 8 + 4 + 1 = 82,
9712 = 942841, 9 + 42 + 8 + 41 = 102.

9712 = 942841 appears in the decimal expression of e:
  e = 2.71828•••942841••• (from the 28871st digit)

Page of Squares : First Upload March 6, 2006 ; Last Revised April 1, 2011
by Yoshio Mimura, Kobe, Japan

972

The smallest squares containing k 972's :
49729 = 2232,
19189729729 = 1385272,
97248649729729 = 98614732.

(745 / 972)2 = 0.587462319... (Komachic).

9722 = 944784, and 9 = 32, 4 = 22, 784 = 282.

3952 + 3962 + 3972 + ... + 9722 = 169152.

(13 + 23 + 33 + 43 + 53 + 63 + 73 + 83)(93) = 9722.

9722 = 93 + 393 + 963.

Komachi equations:
9722 = 92 + 82 - 72 + 62 * 542 * 32 + 22 - 102 = - 92 - 82 + 72 + 62 * 542 * 32 - 22 + 102.

9722 = 944784, 9 + 4 + 4 + 7 + 8 + 4 = 62,
9722 = 944784, 9 + 4 + 47 + 84 = 122,
9722 = 944784, 9 + 44 + 7 + 84 = 122,
9722 = 944784, 94 + 47 + 84 = 152,
9722 = 944784, 94 + 478 + 4 = 242.

Page of Squares : First Upload March 6, 2006 ; Last Revised July 13, 2010
by Yoshio Mimura, Kobe, Japan

973

The smallest squares containing k 973's :
97344 = 3122,
163973973969 = 4049372,
3069739732973824 = 554052322.

9732 is the 10th square which is the sum of 5 fifth powers : 45 + 95 + 105 + 125 + 145.

9732 = 1322 + 4112 + 8722 : 2782 + 1142 + 2312 = 3792,
9732 = 1322 + 4512 + 8522 : 2582 + 1542 + 2312 = 3792.

Komachi equation: 9732 = 983 - 73 * 63 + 53 + 433 - 23 + 13.

9k + 10k + 60k + 90k are squares for k = 1,2,3 (132, 1092, 9732).

9732 + 9742 + 9752 + ... + 30112 = 937942,
9732 + 9742 + 9752 + ... + 3045732 = 970459772.

9732 = 45 + 95 + 105 + 125 + 145.

3-by-3 magic squares consisting of different squares with constant 9732:

A2B2C2
D2E2F2
G2H2K2
where (A, B, C, D, E, F, G, H, K) = 
(3, 548, 804, 684, 573, 388, 692, 564, 387)(8, 219, 948, 339, 888, 208, 912, 332, 69),
(8, 276, 933, 627, 712, 216, 744, 603, 172)(24, 408, 883, 667, 636, 312, 708, 613, 264),
(37, 216, 948, 564, 768, 197, 792, 557, 96)(45, 152, 960, 552, 795, 100, 800, 540, 123),
(48, 388, 891, 429, 792, 368, 872, 411, 132)(63, 462, 854, 658, 609, 378, 714, 602, 273),
(64, 333, 912, 507, 768, 316, 828, 496, 123)(64, 492, 837, 648, 603, 404, 723, 584, 288),
(120, 548, 795, 640, 645, 348, 723, 480, 440)(132, 576, 773, 613, 552, 516, 744, 557, 288),
(141, 408, 872, 648, 692, 219, 712, 549, 372)(144, 307, 912, 492, 816, 197, 827, 432, 276),
(228, 548, 771, 579, 708, 332, 748, 381, 492) 

9732 = 946729, 9 + 4 + 6 + 72 + 9 = 102,
9732 = 946729, 9 + 46 + 729 = 282.

9732 = 946729 appears in the decimal expression of e:
  e = 2.71828•••946729••• (from the 95875th digit).

Page of Squares : First Upload March 6, 2006 ; Last Revised August 17, 2013
by Yoshio Mimura, Kobe, Japan

974

The smallest squares containing k 974's :
169744 = 4122,
23897449744 = 1545882,
974497405397481 = 312169412.

9742 = 948676, a zigzag square.

9742 = 948676, 94 + 8 + 6 + 7 + 6 = 112,
9742 = 948676, 94 + 86 + 76 = 162.

Page of Squares : First Upload March 6, 2006 ; Last Revised October 16, 2006
by Yoshio Mimura, Kobe, Japan

975

The smallest squares containing k 975's :
597529 = 7732,
29757975025 = 1725052,
975397597598736 = 312313562.

9752 is the 4th square which is the sum of 8 seventh powers : 2, 5, 5, 5, 5, 5, 6, 6.

9752 = 950625, with 9 = 32, 50625 = 2252.

9752 = (22 + 9)(42 + 9)(542 + 9).

3-by-3 magic squares consisting of different squares with constant 9752:

A2B2C2
D2E2F2
G2H2K2
where (A, B, C, D, E, F, G, H, K) = 
(0, 240, 945, 585, 756, 192, 780, 567, 144)(0, 273, 936, 375, 864, 252, 900, 360, 105),
(0, 375, 900, 585, 720, 300, 780, 540, 225)(0, 495, 840, 585, 672, 396, 780, 504, 297),
(5, 266, 938, 350, 875, 250, 910, 338, 91)(5, 350, 910, 518, 770, 299, 826, 485, 182),
(10, 181, 958, 550, 790, 155, 805, 542, 94)(10, 314, 923, 430, 827, 286, 875, 410, 130),
(10, 430, 875, 550, 725, 350, 805, 490, 250)(10, 442, 869, 550, 715, 370, 805, 494, 242),
(11, 98, 970, 398, 886, 85, 890, 395, 50)(11, 370, 902, 598, 715, 286, 770, 550, 235),
(22, 235, 946, 571, 770, 178, 790, 550, 155)(24, 468, 855, 657, 624, 360, 720, 585, 300),
(34, 155, 962, 662, 710, 91, 715, 650, 130)(38, 91, 970, 134, 962, 85, 965, 130, 50),
(46, 347, 910, 470, 790, 325, 853, 454, 130)(50, 130, 965, 190, 949, 118, 955, 182, 74),
(50, 190, 955, 395, 878, 154, 890, 379, 122)(50, 218, 949, 650, 715, 130, 725, 626, 182),
(50, 421, 878, 475, 778, 346, 850, 410, 245)(50, 475, 850, 514, 710, 427, 827, 470, 214),
(50, 650, 725, 683, 494, 490, 694, 533, 430)(53, 230, 946, 346, 890, 197, 910, 325, 130),
(74, 350, 907, 610, 725, 230, 757, 550, 274)(85, 470, 850, 542, 731, 350, 806, 442, 325),
(85, 470, 850, 542, 790, 181, 806, 325, 442)(85, 470, 850, 622, 629, 410, 746, 578, 245),
(91, 338, 910, 490, 805, 250, 838, 434, 245)(130, 286, 923, 325, 890, 230, 910, 277, 214),
(130, 325, 910, 410, 850, 245, 875, 350, 250)(130, 325, 910, 533, 790, 206, 806, 470, 283),
(130, 539, 802, 650, 550, 475, 715, 598, 286)(130, 619, 742, 650, 610, 395, 715, 442, 494),
(132, 351, 900, 540, 780, 225, 801, 468, 300)(133, 494, 830, 550, 650, 475, 794, 533, 190),
(142, 406, 875, 581, 742, 250, 770, 485, 350)(181, 442, 850, 542, 731, 350, 790, 470, 325),
(190, 475, 830, 613, 710, 266, 734, 470, 437)(230, 517, 794, 610, 706, 283, 725, 430, 490)

9752 = 950625, 9 + 5 + 0 + 62 + 5 = 92.

Page of Squares : First Upload March 6, 2006 ; Last Revised December 7, 2013
by Yoshio Mimura, Kobe, Japan

976

The smallest squares containing k 976's :
30976 = 1762,
113976976 = 106762,
97689976862976 = 98838242.

The squares which begin with 976 and end in 976 are
9766182976 = 988242,   976491806976 = 9881762,   976784328976 = 9883242,
9760475678976 = 31241762,   9761400456976 = 31243242,...

(939 / 976)2 = 0.925617483... (Komachic).

2552 + 2562 + 2572 + ... + 9762= 174612.

1 / 976 = 0.001024..., and 1024 = 322.

9762 = 952576, 95 + 25 + 76 = 142.

9762 = 952576 appears in the decimal expression of e:
  e = 2.71828•••952576••• (from the 65093rd digit).

Page of Squares : First Upload March 6, 2006 ; Last Revised October 16, 2006
by Yoshio Mimura, Kobe, Japan

977

The smallest squares containing k 977's :
179776 = 4242,
40169779776 = 2004242,
977997776977936 = 312729562.

(374 / 977)2 = 0.146539287... (Komachic).

324 / 8590761 = (6 / 977)2.

9772 = 954529, 954 + 5 + 2 * 9 = 977.

3-by-3 magic squares consisting of different squares with constant 9772:

A2B2C2
D2E2F2
G2H2K2
where (A, B, C, D, E, F, G, H, K) = 
(23, 96, 972, 432, 873, 76, 876, 428, 63)(23, 180, 960, 660, 705, 148, 720, 652, 105),
(36, 408, 887, 447, 796, 348, 868, 393, 216)(41, 348, 912, 672, 652, 279, 708, 639, 212),
(48, 436, 873, 553, 708, 384, 804, 513, 212)(48, 617, 756, 663, 576, 428, 716, 492, 447),
(63, 444, 868, 644, 672, 297, 732, 553, 336)(72, 212, 951, 492, 831, 148, 841, 468, 168),
(76, 513, 828, 567, 652, 456, 792, 516, 247)(96, 337, 912, 687, 672, 176, 688, 624, 303),
(132, 247, 936, 364, 888, 183, 897, 324, 212)(132, 588, 769, 681, 608, 348, 688, 489, 492),
(177, 544, 792, 608, 687, 336, 744, 432, 463)(180, 348, 895, 400, 855, 252, 873, 320, 300),
(183, 392, 876, 492, 804, 257, 824, 393, 348) 

9772 = 954529, 95 + 45 + 29 = 132,
9772 = 954529, 95 + 4529 = 682.

9772 = 954529 appears in the decimal expression of e:
  e = 2.71828•••954529••• (from the 18213rd digit)

Page of Squares : First Upload March 6, 2006 ; Last Revised November 5, 2009
by Yoshio Mimura, Kobe, Japan

978

The smallest squares containing k 978's :
978121 = 9892,
97856978041 = 3128212,
3978978029297881 = 630791412.

9782 = 956484, a zigzag square.

20538k + 169194k + 298290k + 468462k are squares for k = 1,2,3 (9782, 5809322, 3663333722).

The 4-by-4 magic squares consisting of different squares with constant 978:

02 42112292
52232182102
132172222 62
282122 72 12
      
12 72122282
132272 42 82
182 22232112
222142172 32
      
22 32172262
72282 82 92
212 42202112
222132152102

9782 = 956484, 9 + 5 + 6 + 4 + 8 + 4 = 62,
9782 = 956484, 9 + 56 + 4 + 8 + 4 = 92.

Page of Squares : First Upload March 6, 2006 ; Last Revised April 1, 2011
by Yoshio Mimura, Kobe, Japan

979

The smallest squares containing k 979's :
97969 = 3132,
197945797921 = 4449112,
697969795897924 = 264191182.

979 = (12 + 22 + 32 + ... + 442) / (12 + 22 + 32 + 42).

3-by-3 magic squares consisting of different squares with constant 9792:

A2B2C2
D2E2F2
G2H2K2
where (A, B, C, D, E, F, G, H, K) = 
(2, 159, 966, 399, 882, 146, 894, 394, 63)(30, 254, 945, 646, 705, 210, 735, 630, 146),
(38, 369, 906, 486, 794, 303, 849, 438, 214)(42, 306, 929, 511, 786, 282, 834, 497, 126),
(54, 367, 906, 529, 774, 282, 822, 474, 241)(54, 606, 767, 641, 558, 486, 738, 529, 366),
(74, 207, 954, 558, 794, 129, 801, 534, 178)(74, 306, 927, 639, 718, 186, 738, 591, 254),
(81, 254, 942, 578, 774, 159, 786, 543, 214)(81, 282, 934, 362, 879, 234, 906, 326, 177),
(114, 241, 942, 353, 894, 186, 906, 318, 191)(114, 513, 826, 609, 686, 342, 758, 474, 399),
(126, 502, 831, 686, 639, 282, 687, 546, 434)(129, 438, 866, 606, 646, 417, 758, 591, 186),
(178, 486, 831, 534, 753, 326, 801, 394, 402)(222, 399, 866, 434, 834, 273, 849, 322, 366)

Page of Squares : First Upload October 16, 2006 ; Last Revised November 5, 2009
by Yoshio Mimura, Kobe, Japan