Squares:5200s

5200

5200² = (1² + 4)(10² + 4)(14² + 4)(16² + 4) = (1² + 4)(2² + 4)(3² + 4)(14² + 4)(16² + 4)
= (1² + 4)(2² + 4)(3² + 4)(6² + 4)(36² + 4) = (1² + 4)(2² + 4)(4² + 4)(6² + 4)(29² + 4)
= (1² + 4)(3² + 4)(4² + 4)(10² + 4)(14² + 4) = (1² + 4)(6² + 4)(10² + 4)(36² + 4)
= (10² + 4)(14² + 4)(36² + 4) = (2² + 4)(10² + 4)(11² + 4)(16² + 4) = (2² + 4)(16² + 4)(114² + 4)
= (2² + 4)(3² + 4)(14² + 4)(36² + 4) = (2² + 4)(3² + 4)(4² + 4)(10² + 4)(11² + 4)
= (2² + 4)(3² + 4)(4² + 4)(114² + 4) = (2² + 4)(4² + 4)(14² + 4)(29² + 4)
= (3² + 4)(6² + 4)(14² + 4)(16² + 4) = (4² + 4)(10² + 4)(114² + 4).

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

5201

5201² = 38³ + 217³ + 256³.

5201² = 27050401, a zigzag square.

Page of Squares : First Upload November 5, 2007 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5202

5202² = 51⁴ + 51⁴ + 51⁴ + 51⁴.

5202² = 27060804, a zigzag square.

5202² = 27060804, 2² + 7² + 0² + 6² + 0² + 8² + 0² + 4² = 13².

Page of Squares : First Upload November 5, 2007 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5203

5203² = 27071209, a zigzag square.

Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007
by Yoshio Mimura, Kobe, Japan

5204

5204² = 27081616, a zigzag square.

Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007
by Yoshio Mimura, Kobe, Japan

5205

5205² = 4³ + 105³ + 296³.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5207

5207 = (1² + 2² + 3² + ... + 11049²) / (1² + 2² + 3² + ... + 637²).

5207² = 53³ + 237³ + 239³ = 7⁴ + 46⁴ + 58⁴ + 58⁴.

Page of Squares : First Upload September 16, 2008 ; Last Revised November 25, 2008
by Yoshio Mimura, Kobe, Japan

5208

5208² = (1² + 3)(3² + 3)(9² + 3)(82² + 3) = (2² + 3)(3² + 3)(11² + 3)(51² + 3)
= (3² + 3)(11² + 3)(135² + 3) = (9² + 3)(11² + 3)(51² + 3).

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

5209

A cubic polynomial :
(X + 1044²)(X + 2639²)(X + 4368²) = X³ + 5209²X² + 12698868²X + 12034346688².

Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007
by Yoshio Mimura, Kobe, Japan

5211

5211² = 72³ + 186³ + 273³.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5216

5216² = 144³ + 188³ + 260³.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5217

5217² = 24⁴ + 38⁴ + 43⁴ + 68⁴.

The square root of 5217 is 72.228..., and 72 = 2² + 2² + 8².

Page of Squares : First Upload November 5, 2007 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5220

5220² = (1² + 9)(3² + 9)(7² + 9)(51² + 9).

Komachi equations:
5220² = 9² * 87² / 6² * 5² / 4² * 32² */ 1² = 9² * 87² * 6² / 54² * 3² * 2² * 10².

Page of Squares : First Upload October 19, 2010 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

5221

5221² = 27258841 appears in the decimal expressions of π:
π = 3.14159•••27258841••• (from the 32175th digit)
(27258841 is the sixth 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

5223

5223² = 27279729, a zigzag square.

Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007
by Yoshio Mimura, Kobe, Japan

5225

5225⁵ = 3894318555166015625 : 3² + 8² + 9² + 4² + 3² + 18² + 5² + 5² + 5² + 1² + 66² + 0² + 15² + 6² + 2² + 5² = 5225.

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

5226

1326^k + 2730^k + 5226^k + 7618^k are squares for k = 1,2,3 (130², 9724², 779428²).

Page of Squares : First Upload June 17, 2011 ; Last Revised June 17, 2011
by Yoshio Mimura, Kobe, Japan

5229

5229² = 120³ + 174³ + 273³.

5229² = 27342441, 2 * 7 * 342 + 441 = 5229.

Page of Squares : First Upload November 5, 2007 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5232

5232² = 3⁵ + 9⁵ + 20⁵ + 25⁵ + 27⁵.

5232² = 27373824, a zigzag square.

Komachi equation: 5232² = 9² * 8² * 7² * 654² / 3² / 21².

5232² = 27373824, 2 * 7 * 373 + 8 - 2 + 4 = 27 / 3 * 73 * 8 - 24 = 5232.

Page of Squares : First Upload November 5, 2007 ; Last Revised October 19, 2010
by Yoshio Mimura, Kobe, Japan

5234

5234² = 27394756, a zigzag square.

Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007
by Yoshio Mimura, Kobe, Japan

5235

5235² = 1³ + 74³ + 300³.

5235² = 27405225, 2 * 7 - 4 + 0 + 5225 = 5235.

Page of Squares : First Upload November 5, 2007 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5237

5237² = 198³ + 201³ + 226³.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5238

5238² = 129³ + 222³ + 243³.

Komachi equations: 5238² = 9² / 8² / 7² * 6² * 5432² */ 1².

Page of Squares : First Upload September 16, 2008 ; Last Revised October 19, 2010
by Yoshio Mimura, Kobe, Japan

5240

5240² = 27457600, 2 * 74 * 5 * 7 + 60 + 0 = 5240.

Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007
by Yoshio Mimura, Kobe, Japan

5242

5242² = 8³ + 219³ + 257³.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5243

5243² = 77³ + 231³ + 245³.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5244

5244² = 122³ + 186³ + 268³.

5244² = 27499536, 2 - 7 - 4 + 99 * 53 + 6 = 5244.

Page of Squares : First Upload November 5, 2007 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5246

5246² = 27520516, 2² + 7² + 5² + 2² + 0² + 5² + 1² + 6² = 12².

5246² = (13² + 3)(400² + 3).

Page of Squares : First Upload November 5, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

5247

5247² = 12⁴ + 18⁴ + 27⁴ + 72⁴.

5247² = 27531009, 2² + 7² + 5² + 3² + 1² + 0² + 0² + 9² = 13².

Page of Squares : First Upload November 5, 2007 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5248

5248² = 8⁴ + 24⁴ + 24⁴ + 72⁴.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5250

5250² = (1² + 6)(12² + 6)(162² + 6) = (1² + 6)(2² + 6)(3² + 6)(12² + 6)(13² + 6)
= (1² + 6)(2² + 6)(3² + 6)(162² + 6) = (3² + 6)(8² + 6)(12² + 6)(13² + 6)
= (3² + 6)(8² + 6)(162² + 6).

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

5251

5251^k + 7257^k + 15635^k + 27553^k are squares for k = 1,2,3 (236², 32922², 5026564²).

Page of Squares : First Upload June 17, 2011 ; Last Revised June 17, 2011
by Yoshio Mimura, Kobe, Japan

5252

5252² = 27583504, a zigzag square.

Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007
by Yoshio Mimura, Kobe, Japan

5253

5253² = 27594009, 2² + 7² + 5² + 9² + 4² + 0² + 0² + 9² = 16².

5253² + 5254² + 5255² + ... + 5304² = 5305² + 5306² + 5307² + ... + 5355².

Page of Squares : First Upload November 5, 2007 ; Last Revised September 16, 2011
by Yoshio Mimura, Kobe, Japan

5255

5255² = 27615025, 2² + 7² + 6² + 1² + 5² + 0² + 2² + 5² = 12².

Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007
by Yoshio Mimura, Kobe, Japan

5256

5256²± 5 are primes.

5256² = 72³ + 142³ + 290³.

5256² = 27625536, 2 * 7 * 625 / 5 * 3 + 6 = 5256.

Page of Squares : First Upload November 5, 2007 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

5257

5257² = 193³ + 201³ + 231³.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5258

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

Page of Squares : First Upload June 17, 2011 ; Last Revised June 17, 2011
by Yoshio Mimura, Kobe, Japan

5259

Komachi equation: 5259² = 9² * 8765² * 4² / 3² / 2² / 10².

Page of Squares : First Upload October 19, 2010 ; Last Revised October 19, 2010
by Yoshio Mimura, Kobe, Japan

5265

5265² = 33³ + 156³ + 288³.

Komachi equation: 5265² = 12² * 3² / 4² * 5² / 6² * 78² * 9².

Page of Squares : First Upload September 16, 2008 ; Last Revised October 19, 2010
by Yoshio Mimura, Kobe, Japan

5270

1666^k + 2210^k + 5270^k + 9350^k are squares for k = 1,2,3 (136², 11084², 989536²).
496^k + 5270^k + 7161^k + 11098^k are squares for k = 1,2,3 (155², 14229², 1371347²).

Page of Squares : First Upload June 17, 2011 ; Last Revised June 17, 2011
by Yoshio Mimura, Kobe, Japan

5273

1 / 5273 = 0.0001896453631, 1² + 8² + 9² + 64² + 5² + 3² + 6² + 31² = 5273.

Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007
by Yoshio Mimura, Kobe, Japan

5277

5277² = 25³ + 66³ + 302³.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5278

5278² = 57³ + 98³ + 299³.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5280

5280² = (11² - 1)(21² - 1)(23² - 1) = (3² - 1)(21² - 1)(89² - 1) = (3² - 1)(4² - 1)(21² - 1)(23² - 1)
= (3² - 1)(9² - 1)(10² - 1)(21² - 1) = (4² - 1)(21² - 1)(65² - 1).

5280² = 145³ + 146³ + 279³.

The integral triangle of sides 697, 131144, 131697 has square area 5280².

122² + 5280 = 142², 122² - 5280 = 98²,
73² + 5280 = 103², 73² - 5280 = 7².

The square root of 5280 is 72.66..., 72 = 6² + 6².

Page of Squares : First Upload November 5, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

5281

5281² = 27888961, 2 - 7 * 8 + 889 * 6 + 1 = 5281.

Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007
by Yoshio Mimura, Kobe, Japan

5282

5282² = 27899524, 2² + 7² + 8² + 9² + 9² + 5² + 2² + 4² = 18².

Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007
by Yoshio Mimura, Kobe, Japan

5283

5283² = 66³ + 220³ + 257³ = 129³ + 178³ + 272³.

Page of Squares : First Upload September 16, 2008 ; Last Revised September 16, 2008
by Yoshio Mimura, Kobe, Japan

5286

5286²± 5 are primes.

5286² = (2² + 2)(2158² + 2).

Page of Squares : First Upload December 28, 2013 ; Last Revised January 18, 2014
by Yoshio Mimura, Kobe, Japan

5287

5287² = 27952369, 2² + 7² + 9² + 5² + 2² + 3² + 6² + 9² = 17².

Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007
by Yoshio Mimura, Kobe, Japan

5288

5288² = 27962944, 27 / 9 * 6 * 294 - 4 = 5288.

Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007
by Yoshio Mimura, Kobe, Japan

5289

5289² = (6² + 5)(826² + 5).

5289^k + 9202^k + 12986^k + 18748^k are squares for k = 1,2,3 (215², 25155², 3115565²).

Page of Squares : First Upload June 17, 2011 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

5292

5292² = (1² + 5)(2² + 5)(3² + 5)(11² + 5)(17² + 5) = (1² + 5)(3² + 5)(4² + 5)(7² + 5)(17² + 5)
= (3² + 5)(7² + 5)(11² + 5)(17² + 5).

5292² = 84³ + 126³ + 294³ = 102³ + 222³ + 252³.

5292² = 28005264, 28 + 0 + 0 + 5264 = 28 + 0 * 0 + 5264 = 5292.

Page of Squares : First Upload November 5, 2007 ; Last Revised December 28, 2013
by Yoshio Mimura, Kobe, Japan

5294

5294² = 28026436, 2² + 8² + 0² + 2² + 6² + 4² + 3² + 6² = 13².

Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007
by Yoshio Mimura, Kobe, Japan

5298

5298² = 28068804, a square with even digits.

Page of Squares : First Upload November 5, 2007 ; Last Revised November 5, 2007
by Yoshio Mimura, Kobe, Japan