Squares:1700s

1700

1700² = (1² + 1)(3² + 1)(4² + 1)(7² + 1)(13² + 1).

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

1701

1701² = 2893401, a square with different digits.

1701² = 9³ + 84³ + 132³.

Komachi equations:
1701² = 1² * 2² / 3² * 4² * 567² / 8² * 9² = 1² / 2² / 3² / 4² * 567² * 8² * 9²
= 9² / 8² * 7² * 6² * 54² / 3² * 2² */ 1².

1701² = (1)(2 + 3 + 4 + ... + 19)(20 + 21 + 22)(23 + 24 + 25 + ... + 31),
1701² = (1 + 2)(3 + 4)(5 + 6 + 7 + ... + 22)(23 + 24 + 25 + ... + 40).

Page of Squares : First Upload February 19, 2007 ; Last Revised September 7, 2010
by Yoshio Mimura, Kobe, Japan

1702

1702² = 2896804, 2 + 896 + 804 = 1702.

1702² = 33³ + 100³ + 123³.

Page of Squares : First Upload February 19, 2007 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1703

1703 = (1² + 2² + 3² + ... + 65²) / (1² + 2² + 3² + 4² + 5²).

1703² = 2900209, a square with just 3 kinds of digits.

1703² = 12⁴ + 22⁴ + 24⁴ + 39⁴.

Page of Squares : First Upload February 19, 2007 ; Last Revised November 25, 2008
by Yoshio Mimura, Kobe, Japan

1704

1704² = 56³ + 100³ + 120³.

The quadratic polynomial -1704X² + 150528X - 22799 takes the values 355², 521², 643², 743², 829², 905² at X = 1, 2,..., 6,

Page of Squares : First Upload July 14, 2008 ; Last Revised December 15, 2008
by Yoshio Mimura, Kobe, Japan

1705

1705 = (1² + 2² + 3² + ... + 77²) / (1² + 2² + 3² + 4² + 5² + 6²).

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

1706

1706² = 2910436, a square with different digits.

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1708

1708² = 2917264, a zigzag square.

154^k + 490^k + 1708^k + 3577^k are squares for k = 1,2,3 (77², 3997², 225547²).

Page of Squares : First Upload February 19, 2007 ; Last Revised May 6, 2011
by Yoshio Mimura, Kobe, Japan

1709

1709² = 1³ + 74³ + 136³.

A cubic polynomial:
(X + 348²)(X + 539²)(X + 1584²) = X³ + 1709²X² + 1033428²X + 297114048².

Page of Squares : First Upload February 19, 2007 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1710

1710² = 2⁸ + 2⁸ + 3⁸ + 4⁸ + 5⁸ + 5⁸ + 5⁸ + 6⁸.

1710² = (1)(2)(3)(4 + 5 + 6 + ... + 41)(42 + 43 + 44 + ... + 53),
1710² = (1)(2 + 3)(4 + 5)(6 + 7 + 8 + ... + 13)(14 + 15 + 16 + ... + 43),
1710² = (1)(2 + 3)(4 + 5)(6 + 7 + 8 + ... + 24)(25 + 26 + 27 + ... + 32),
1710² = (1)(2 + 3)(4 + 5)(6 + 7 + 8 + 9)(10 + 11 + 12 + ... + 66),
1710² = (1)(2 + 3)(4 + 5 + 6 + 7 + 8)(9)(10 + 11 + 12 + ... + 66),
1710² = (1)(2 + 3)(4 + 5 + 6 + 7 + 8)(9 + 10)(11 + 12 + 13 + ... + 46),
1710² = (1)(2 + 3)(4 + 5 + 6 + 7 + 8)(9 + 10 + 11 + ... + 27)(28 + 29),
1710² = (1)(2 + 3 + 4 + ... + 28)(29 + 30 + 31 + ... + 123),
1710² = (1)(2 + 3 + 4 + 5 + 6)(7 + 8)(9)(10 + 11 + 12 + ... + 47),
1710² = (1)(2 + 3 + 4)(5)(6 + 7 + 8 + ... + 13)(14 + 15 + 16 + ... + 43),
1710² = (1)(2 + 3 + 4)(5)(6 + 7 + 8 + ... + 24)(25 + 26 + 27 + ... + 32),
1710² = (1)(2 + 3 + 4)(5)(6 + 7 + 8 + 9)(10 + 11 + 12 + ... + 66),
1710² = (1 + 2 + 3)(4 + 5 + 6 + ... + 41)(42 + 43 + 44 + ... + 53).

Page of Squares : First Upload February 19, 2007 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1711

1711 = (1² + 2² + 3² + ... + 29²) / (1² + 2²).

1711² = 1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 7³ + ... + 58³.

1711² + 1712² + 1713² + ... + 1740² = 1741² + 1742² + 1743² + ... + 1769².

Page of Squares : First Upload February 19, 2007 ; Last Revised September 9, 2011
by Yoshio Mimura, Kobe, Japan

1713

1713² = (1² + 2)(989² + 2).

Page of Squares : First Upload December 14, 2013 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

1716

1716² = 40³ + 78³ + 134³.

1716^k + 2184^k + 6097^k + 10452^k are squares for k = 1,2,3 (143², 12415², 1176409²).
481^k + 624^k + 1404^k + 1716^k are squares for k = 1,2,3 (65², 2353², 90415²).

The integral triangle of sides 1859, 3232, 4035 has square area 1716².

1716² = (1)(2)(3)(4)(5 + 6)(7 + 8 + 9 + ... + 149),
1716² = (1)(2)(3 + 4 + 5 + ... + 10)(11)(12 + 13 + 14)(15 + 16 + 17 + 18),
1716² = (1 + 2 + 3 + ... + 12)(13 + 14 + 15 + ... + 20)(21 + 22 + 23 + ... + 31),
1716² = (1 + 2 + 3 + ... + 32)(33 + 34 + 35 + ... + 110),
1716² = (1 + 2 + 3)(4)(5 + 6)(7 + 8 + 9 + ... + 149).

Page of Squares : First Upload February 19, 2007 ; Last Revised October 7, 2011
by Yoshio Mimura, Kobe, Japan

1719

Komachi equation: 1719² = 9⁴ - 8⁴ + 7⁴ * 6⁴ + 5⁴ + 4⁴ - 3⁴ - 2⁴ * 10⁴.

Page of Squares : First Upload September 7, 2010 ; Last Revised September 7, 2010
by Yoshio Mimura, Kobe, Japan

1720

1720² = 76³ + 108³ + 108³.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1722

1722² = 23⁴ + 23⁴ + 27⁴ + 37⁴.

1722² = (1² + 5)(703² + 5).

Page of Squares : First Upload July 14, 2008 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

1725

1725² = 25³ + 60³ + 140³.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1726

1726² = 2979076, a zigzag square.

The square root of 1726 is 41.54..., and 41 = 5² + 4².

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1727

537097^k + 735702^k + 818598^k + 891132^k are squares for k = 1,2,3 (1727², 1514579², 1345120579²).

Page of Squares : First Upload May 6, 2011 ; Last Revised May 6, 2011
by Yoshio Mimura, Kobe, Japan

1728

1728² = 1³ + 71³ + 138³ = 16³ + 96³ + 128³ = 68³ + 78³ + 130³ = 72³ + 96³ + 120³.

A cubic plynomial :
(X + 528²)(X + 1728²)(X + 62771²) = X³ + 62797²X² + 113422512²X + 57271256064².

Komachi equations:
1728² = - 9² * 8² * 7² + 6² * 5² * 4² * 3² / 2² * 10²,
1728² = 12³ / 3³ * 4³ * 56³ / 7³ / 8³ * 9³ = 12³ / 3³ * 4³ / 56³ * 7³ * 8³ * 9³.

Page of Squares : First Upload February 19, 2007 ; Last Revised September 7, 2010
by Yoshio Mimura, Kobe, Japan

1729

1729² = 181³ - 180³ + 179³ - 178³ + 177³ - ... + 1³.

665665^k + 681226^k + 795340^k + 847210^k are squares for k = 1,2,3 (1729², 1502501², 1312364599²).

Page of Squares : First Upload February 19, 2007 ; Last Revised May 6, 2011
by Yoshio Mimura, Kobe, Japan

1730

1730² = 2992900, 2 + 9 * 92 + 900 = 1730.

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1731

1731² = 2996361, 2 + 9 * 96 / 3 * 6 + 1 = 2 * 9 * 96 - 3 + 6 * 1 = 1731.

411978^k + 586809^k + 682014^k + 1315560^k are squares for k = 1,2,3 (1731², 1646181², 1692943965²).

Page of Squares : First Upload February 19, 2007 ; Last Revised May 6, 2011
by Yoshio Mimura, Kobe, Japan

1732

1732² = 4⁴ + 28⁴ + 32⁴ + 34⁴.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1734

1 / 1734 = 0.000576..., and 576 = 24².

1734² = (7² + 2)(10² + 2)(24² + 2).

Page of Squares : First Upload February 19, 2007 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

1735

1 / 1735 = 0.000576..., and 576 = 24².

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1736

1 / 1736 = 0.000576..., and 576 = 24².

1736²= 127 x 128 + 128 x 129 + 129 x 130 + 130 x 131 + 131 x 132 + ... + 222 x 223.

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1737

1737² = 3017169, 30 + 1716 - 9 = 1737.

1737²± 2 are primes.

Page of Squares : First Upload February 19, 2007 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe, Japan

1738

1738² = 3020644, 3² + 0² + 2² + 0² + 6² + 4² + 4² = 9².

1276^k + 1529^k + 1738^k + 5258^k are squares for k = 1,2,3 (99², 5885², 395307²).

Page of Squares : First Upload February 19, 2007 ; Last Revised May 6, 2011
by Yoshio Mimura, Kobe, Japan

1739

1739 = (1² + 2² + 3² + ... + 258²) / (1² + 2² + 3² + ... + 21²).

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

1740

Komachi equations: 1740² = 9² * 87² / 6² * 5² * 4² / 3² * 2² */ 1².

Page of Squares : First Upload September 7, 2010 ; Last Revised September 7, 2010
by Yoshio Mimura, Kobe, Japan

1741

1741⁴ = 9187452028561, and 9² + 18² + 7² + 4² + 5² + 20² + 28² + 5² + 6² + 1² = 1741.

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

1742

260^k + 286^k + 1742^k + 5993^k are squares for k = 1,2,3 (91², 6253², 469651²).

Page of Squares : First Upload May 6, 2011 ; Last Revised May 6, 2011
by Yoshio Mimura, Kobe, Japan

1743

1743² = 50³ + 97³ + 126³.

1743⁵ = 16087439829116943 :
16² + 0² + 8² + 7² + 4² + 3² + 9² + 8² + 29² + 1² + 16² + 9² + 4² + 3² = 1743.

Page of Squares : First Upload July 14, 2008 ; Last Revised December 8, 2008
by Yoshio Mimura, Kobe, Japan

1744

1744² = 3041536, a zigzag square.

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1745

1745 = (1² + 2² + 3² + ... + 174²) / (1² + 2² + 3² + ... + 14²).

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

1746

1746² = 3048516, a square with different digits.

1746² = 3048516, 30 * 48 + 51 * 6 = 1746.

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1748

1748² = 3055504, 3² + 0² + 5² + 5² + 5² + 0² + 4² = 10².

1748³ = 5341020992, and 5² + 34² + 1² + 0² + 20² + 9² + 9² + 2² = 1748.

Page of Squares : First Upload February 19, 2007 ; Last Revised December 1, 2008
by Yoshio Mimura, Kobe, Japan

1749

1749²± 2 are primes.

1749² = 1³ + 110³ + 120³ = 16³ + 41³ + 144³.

88^k + 638^k + 1122^k + 1177^k are squares for k = 1,2,3 (55², 1749², 57475²).

Page of Squares : First Upload July 14, 2008 ; Last Revised December 29, 2013
by Yoshio Mimura, Kobe, Japan

1750

1750² = (3 + 4 + 5 + 6 + 7)² + (8 + 9 + 10 + 11 + 12)² + (13 + 14 + 15 + 16 + 17)² + ... + (118 + 119 + 120 + 121 + 122)².

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1751

Komachi equation: 1751² = 98³ - 7³ + 6³ * 5³ + 4³ * 32³ + 10³.

Page of Squares : First Upload September 7, 2010 ; Last Revised September 7, 2010
by Yoshio Mimura, Kobe, Japan

1755

1755² = 24³ + 26³ + 145³ = 3⁶ + 6⁶ + 6⁶ + 12⁶.

1755² = (74 + 75 + 76)² + (77 + 78 + 79)² + (80 + 81 + 82)² + ... + (149 + 150 + 151)².

1755², 4576², 6732², 1755² + 4576², 4576² + 6732², and 6732² + 1755² are squares.

1755² = (1)(2 + 3)(4 + 5)(6 + 7 + 8 + ... + 20)(21 + 22 + 23 + ... + 33),
1755² = (1)(2 + 3 + 4)(5)(6 + 7 + 8 + ... + 20)(21 + 22 + 23 + ... + 33),
1755² = (1 + 2)(3)(4 + 5 + 6)(7 + 8 + 9 + ... + 19)(20 + 21 + 22 + ... + 25),
1755² = (1 + 2 + 3 + ... + 26)(27)(28 + 29 + 30 + ... + 37).

Page of Squares : First Upload February 19, 2007 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1756

1756² = 3083536, a zigzag square.

1756² = 6³ + 46³ + 144³ = 28³ + 102³ + 126³.

1756² = 3083536 appears in the decimal expressions of e:
e = 2.71828•••3083536••• (from the 25078th digit)
(3083536 is the seventh 7-digit square in the expression of e.)

Page of Squares : First Upload February 19, 2007 ; Last Revised November 4, 2008
by Yoshio Mimura, Kobe, Japan

1758

1758² = 46³ + 75³ + 137³.

279522^k + 666282^k + 750666^k + 1394094^k are squares for k = 1,2,3 (1758², 1740420², 1857428964²).

Page of Squares : First Upload July 14, 2008 ; Last Revised May 6, 2011
by Yoshio Mimura, Kobe, Japan

1760

1760² = (2³ + 3)(5³ + 3)(13³ + 3).

Komachi equations:
1760² = 9⁴ - 8⁴ + 7⁴ * 6⁴ - 54⁴ / 3⁴ / 2⁴ - 10⁴ = - 9⁴ - 8⁴ + 7⁴ * 6⁴ + 54⁴ / 3⁴ / 2⁴ - 10⁴.

Page of Squares : First Upload September 7, 2010 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

1762

(1762² - 4) = (5² - 4)(6² - 4)(8² - 4)(9² - 4) = (3² - 4)(4² - 4)(5² - 4)(6² - 4)(9² - 4).

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1763

Komachi equation: 1763² = 98³ + 76³ + 5³ * 4³ * 3³ * 2³ + 1³.

Page of Squares : First Upload September 7, 2010 ; Last Revised September 7, 2010
by Yoshio Mimura, Kobe, Japan

1764

The square of 42.

1764² = 49³ + 63³ + 140³.

1764² = (1² + 5)(3² + 5)(11² + 5)(17² + 5).

1764² = (1)(2)(3 + 4 + 5 + ... + 9)(10 + 11)(12 + 13 + 14 + ... + 60),
1764² = (1)(2)(3 + 4 + 5 + ... + 9)(10 + 11 + 12 + ... + 17)(18 + 19 + 20 + ... + 31),
1764² = (1)(2)(3 + 4 + 5 + ... + 9)(10 + 11 + 12 + ... + 18)(19 + 20 + 21 + ... + 30),
1764² = (1)(2 + 3 + 5 + ... + 10)(11 + 12 + 13 + ... + 17)(18 + 19 + 20 + ... + 38),
1764² = (1)(2 + 3 + 4 + 5)(6)(7 + 8 + 9 + ... + 20)(21 + 22 + 23 + ... + 28),
1764² = (1 + 2 + 3 + ... + 7)(8 + 9 + 10 + ... + 13)(14)(15 + 16 + 17 + ... + 21).

Page of Squares : First Upload February 19, 2007 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

1765

1765² = 33³ + 60³ + 142³ = 78³ + 97³ + 120³.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1766

1766² = 3118756, 31 * 1 * 8 * 7 + 5 * 6 = 1766.

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1767

1767² = 7⁴ + 8⁴ + 8⁴ + 42⁴.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1769

1769² = 3129361, 3 * 1 * 29 / 3 * 61 = 1769.

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1770

1770² = 1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 7³ + ... + 59³.

1770² = (79 + 80 + 81)² + (82 + 83 + 84)² + (85 + 86 + 87)² + ... + (151 + 152 + 153)².

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1771

1771² = (35 + 36 + 37 + 38 + 39 + 40 + 41)² + (42 + 43 + 44 + 45 + 46 + 47 + 48)² + (49 + 50 + 51 + 52 + 53 + 54 + 55)² + ... + (105 + 106 + 107 + 108 + 109 + 110 + 111)².

1771² = 3136441, and 3136 = 56², 441 = 21².

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1773

1773² = 3143529, a zigzag square.

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1775

1775² = 3150625, a zigzag square.

1775² = 3150625, 3² + 1² + 5² + 0² + 6² + 2² + 5² = 10².

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1776

1776² = 3154176, 31 * 54 + 17 * 6 = 1776.

1776² = 12³ + 47³ + 145³.

Page of Squares : First Upload February 19, 2007 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1777

1777² = 33³ + 116³ + 116³ = 36³ + 89³ + 134³ = 16⁴ + 29⁴ + 32⁴ + 34⁴.

The square root of 1777 is 42.154, and 42 = 1² + 5² + 4².

1777² = 3157729 appears in the decimal expressions of e:
e = 2.71828•••3157729••• (from the 96427th digit)

Page of Squares : First Upload February 19, 2007 ; Last Revised November 4, 2008
by Yoshio Mimura, Kobe, Japan

1779

1779² = 64³ + 65³ + 138³.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1781

Loop of length 5 (See 41):
1781 -- 17² + 81² = 6850 -- 68² + 50² = 7124 -- 71² + 24² = 5617 -- 56² + 17² = 3425 - 34² + 25² = 1781

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

1782

1782² = 3175524, 3 + 1755 + 24 = 1782.

1782² = (1² + 2)(2² + 2)(19² + 2)(22² + 2).

1782² = (1)(2)(3)(4 + 5 + 6 + 7)(8 + 9 + 10 + ... + 25)(26 + 27 + 28),
1782² = (1)(2)(3)(4 + 5 + 6 + 7)(8 + 9 + 10)(11 + 12 + 13 + ... + 43),
1782² = (1)(2 + 3 + 4 + ... + 7)(8 + 9 + 10 + ... + 16)(17 + 18 + 19 + ... + 49),
1782² = (1 + 2)(3)(4 + 5)(6)(7 + 8 + 9 + ... + 114),
1782² = (1 + 2)(3)(4 + 5 + 6 + 7)(8 + 9 + 10)(11)(12 + 13 + 14 + 15),
1782² = (1 + 2)(3 + 4 + 5 + 6)(7 + 8 + 9 + ... + 15)(16 + 17)(18),
1782² = (1 + 2 + 3)(4 + 5 + 6 + 7)(8 + 9 + 10 + ... + 25)(26 + 27 + 28),
1782² = (1 + 2 + 3)(4 + 5 + 6 + 7)(8 + 9 + 10)(11 + 12 + 13 + ... + 43) = (1² + 2)(2² + 2)(4² + 2)(5² + 2)(19² + 2) = (1² + 2)(3² + 2)(14² + 2)(22² + 2) = (1² + 2)(3² + 2)(4² + 2)(5² + 2)(14² + 2) = (2² + 2)(5² + 2)(140² + 2) = (4² + 2)(19² + 2)(22² + 2).

Page of Squares : First Upload February 19, 2007 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

1784

1784² = 3182656, a zigzag square.

1784²± 3 are primes.

Page of Squares : First Upload February 19, 2007 ; Last Revised January 16, 2014
by Yoshio Mimura, Kobe, Japan

1785

1785² = 1³ + 42³ + 146³ = 83³ + 91³ + 123³.

990^k + 1020^k + 1785^k + 1830^k are squares for k = 1,2,3 (75², 2925², 117675²).

Page of Squares : First Upload July 14, 2008 ; Last Revised May 6, 2011
by Yoshio Mimura, Kobe, Japan

1786

1786²± 3 are primes.

1786² = 353² + 354² + 355² + 356² + 357² + 358² + 359² + ... + 376².

1786² = 36³ + 83³ + 137³.

Page of Squares : First Upload February 19, 2007 ; Last Revised January 16, 2014
by Yoshio Mimura, Kobe, Japan

1791

1791² = 3207681, a square with different digits.

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1792

1792² = 88³ + 104³ + 112³ = 16⁴ + 32⁴ + 32⁴ + 32⁴ = 8⁵ + 8⁵ + 16⁵ + 16⁵ + 16⁵.

1792² = (1² + 7)(3² + 7)(7² + 7)(21² + 7) = (7² + 7)(11² + 7)(21² + 7).

Komachi eqations: 1792² = 9² * 8² * 7² * 6² / 54² * 32² */ 1².

Page of Squares : First Upload September 7, 2010 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

1793

1793² = 4⁴ + 8⁴ + 34⁴ + 37⁴.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan

1794

1794^k + 3250^k + 12402^k + 15678^k are squares for k = 1,2,3 (182², 20332², 2408588²).
130^k + 1794^k + 6994^k + 7982^k are squares for k = 1,2,3 (130², 10764², 925444²).

Page of Squares : First Upload May 6, 2011 ; Last Revised May 6, 2011
by Yoshio Mimura, Kobe, Japan

1795

1795² = 3222025, a square by pegged 2.

Page of Squares : First Upload February 19, 2007 ; Last Revised February 19, 2007
by Yoshio Mimura, Kobe, Japan

1797

440265^k + 636138^k + 1027884^k + 1124922^k are squares for k = 1,2,3 (1797², 1708947², 1688876307²).

Page of Squares : First Upload May 6, 2011 ; Last Revised May 6, 2011
by Yoshio Mimura, Kobe, Japan

1798

1798² = 3232804, a zigzag square.

1798² = S₂(6727) / S₂(45), where S₂(n) = 1² + 2² + 3² + ... +n².

1798^k + 6882^k + 25110^k + 27714^k are squares for k = 1,2,3 (248², 38068², 6119648²).

Page of Squares : First Upload February 19, 2007 ; Last Revised May 6, 2011
by Yoshio Mimura, Kobe, Japan

1799

1799² = 25³ + 84³ + 138³ = 25³ + 112³ + 122³.

Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008
by Yoshio Mimura, Kobe, Japan