Squares:27000s

27000

195² + 27000 = 255², 195² - 27000 = 105².

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27030

27030² = (1² + 9)(5² + 9)(16² + 9)(90² + 9) = (9² + 9)(16² + 9)(175² + 9).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27044

27044² = 731377936, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

27058

27058²± 3 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27073

27073² = 732947329.

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27081

27081² = (1² + 2)(7² + 2)(23² + 2)(95² + 2).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27090

27090² = (2² + 5)(9² + 5)(10² + 5)(95² + 5) = (5² + 5)(52² + 5)(95² + 5)
= (5² + 5)(9² + 5)(10² + 5)(52² + 5).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27104

27104² = (1² + 7)(35² + 7)(273² + 7) = (2² + 7)(3² + 7)(7² + 7)(273² + 7)
= (2² + 7)(7² + 7)(31² + 7)(35² + 7) = (7² + 7)(13² + 7)(273² + 7).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27105

27105² = 734681025 is a square with different digits.

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27124

27124² = 735711376, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

27129

27129² = 735982641 is a square with different digits.

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27146

27146² = (2² + 3)(44² + 3)(233² + 3).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27152

27152²± 3 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27154

27154² = 737339716, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

27166

27166² = 737991556, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

27175

27176² = (25² + 7)(1081² + 7).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27209

27209² = 740329681 is a square with different digits.

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27216

15⁴ + 27216 = 279², 15⁴ - 27216 = 153².

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27222

27222²± 5 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27225

27225 = 165² is a square with 3 kinds of digits.

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27234

27234² = (1² + 2)(7² + 2)(10² + 2)(218² + 2) = (12² + 9)(13² + 9)(165² + 9)
= (5² + 2)(24² + 2)(218² + 2).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27258

27258²± 5 are primes.

27258² = (6² + 6)(4206² + 6).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27273

27273² = 743816529 is a square with different digits.

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27306

27306² = (18² + 9)(27² + 9)(55² + 9).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27360

27360² = (19² - 1)(37² - 1)(39² - 1) = (2² - 1)(11² - 1)(37² - 1)(39² - 1)
= (2² - 1)(3² - 1)(37² - 1)(151² - 1) = (2² - 1)(3² - 1)(4² - 1)(37² - 1)(39² - 1)
= (4² - 1)(37² - 1)(191² - 1) = (4² - 1)(5² - 1)(37² - 1)(39² - 1) = (5² - 1)(37² - 1)(151² - 1).

362² + 27360 = 398², 362² - 27360 = 322².

Page of Squares : First Upload April 21, 2012 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27365

27365² = (2² + 1)(12238² + 1).

Page of Squares : First Upload November 9, 2013 ; Last Revised November 9, 2013
by Yoshio Mimura, Kobe, Japan

27370

27370²± 3 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27375

27375² = (8² + 9)(3204² + 9).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27378

27378² = 303² + 305² + 307² + 309² + 311² + 313² + ... + 1653².

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27379

27379² = 749609641, and 74960964 = 8658², 1 = 1².

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27392

27392² = (3² + 7)(5² + 7)(10² + 7)(117² + 7).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27396

27396²± 5 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27405

27405² = (2² - 1)(4² - 1)(28² - 1)(146² - 1).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27422

27422²± 3 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27444

27444² = 753173136, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

27450

27450² = (1² + 9)(3² + 9)(2046² + 9).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27456

290² + 27456 = 334², 290² - 27456 = 238².

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27462

27462²± 5 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27472

27472² = 1266 x 1267 + 1268 x 1269 + 1270 x 1271 + 1272 x 1273 + ... + 1870 x 1871.

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27477

27477²± 2 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27500

5⁷ + 27500 = 325², 5⁷ - 27500 = 225².

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27532

27532²± 3 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27540

27540² is the sum of consecutive primes (3 + 5 + 7 + 11 + ... + 130729).

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27556

27556² = 759333136, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

27560

27560² = (1² + 4)(2² + 4)(3² + 4)(7² + 4)(166² + 4) = (1² + 4)(3² + 4)(7² + 4)(10² + 4)(46² + 4)
= (1² + 4)(7² + 4)(10² + 4)(166² + 4) = (2² + 4)(7² + 4)(29² + 4)(46² + 4)
= (3² + 4)(46² + 4)(166² + 4) = (3² + 4)(6² + 4)(7² + 4)(166² + 4).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27582

27582²± 5 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27588

27588² = (2² + 8)(50² + 8)(159² + 8) = (2² + 8)(6² + 8)(7² + 8)(159² + 8)
= (5² + 8)(38² + 8)(126² + 8) = (6² + 8)(26² + 8)(159² + 8) = (6² + 8)(50² + 8)(83² + 8).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27600

27600² = (24² - 1)(1151² - 1).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27602

27602²± 3 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27609

27609²± 2 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27621

27621²± 2 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27640

27640²± 3 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27664

27664² = (1² + 3)(2² + 3)(5² + 3)(7² + 3)(137² + 3) = (1² + 3)(4² + 3)(7² + 3)(19² + 3)(23² + 3)
= (1² + 3)(5² + 3)(19² + 3)(137² + 3).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27696

27696² = (2² + 8)(4² + 8)(1632² + 8).

The quadratic polynomial 27696X² - 93096X + 90049 takes the values 157², 121², 245², 401², 563², 727² at X = 1, 2,..., 6,

Page of Squares : First Upload April 21, 2012 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27713

27713² = 3185² + 3186² + 3187² + ... + 3258².

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27720

27720² = 2751 x 2752 + 2752 x 2753 + 2753 x 2754 +...+ 2848 x 2849.

27720² = (19² - 1)(34² - 1)(43² - 1) = (2² - 1)(11² - 1)(34² - 1)(43² - 1)
= (2² - 1)(3² - 1)(4² - 1)(34² - 1)(43² - 1) = (2² - 1)(3² - 1)(8² - 1)(21² - 1)(34² - 1)
= (2² - 1)(4² - 1)(21² - 1)(197² - 1) = (2² - 1)(5² - 1)(43² - 1)(76² - 1)
= (2² - 1)(6² - 1)(10² - 1)(13² - 1)(21² - 1) = (3² - 1)(10² - 1)(13² - 1)(76² - 1)
= (3² - 1)(10² - 1)(29² - 1)(34² - 1) = (3² - 1)(4² - 1)(6² - 1)(10² - 1)(43² - 1)
= (3² - 1)(5² - 1)(6² - 1)(10² - 1)(34² - 1) = (3² - 1)(6² - 1)(8² - 1)(10² - 1)(21² - 1)
= (4² - 1)(5² - 1)(34² - 1)(43² - 1) = (4² - 1)(8² - 1)(21² - 1)(43² - 1)
= (5² - 1)(8² - 1)(21² - 1)(34² - 1) = (6² - 1)(10² - 1)(11² - 1)(43² - 1)
= (6² - 1)(43² - 1)(109² - 1) = (8² - 1)(10² - 1)(351² - 1).

Page of Squares : First Upload April 21, 2012 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27732

27732² = 3³ + 5³ + 24³ + 78³ + 916³

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27740

27740²± 3 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27744

170² + 27744 = 238², 170² - 27744 = 34².

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27749

27749² = 770007001 is a square with 3 kinds of digits.

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27750

27750² = (18² + 9)(19² + 9)(79² + 9) = (79² + 9)(351² + 9).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27762

27762² = 5219 x 5220 + 5221 x 5222 + 5223 x 5224 + 5225 x 5226 + ... + 5273 x 5274.

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27790

27790² = 270 x 271 + 272 x 273 + 274 x 275 + 276 x 277 + ... + 1668 x 1669.

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27795

27795²± 2 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27808

27808² = (1² + 7)(2² + 7)(11² + 7)(262² + 7) = (1² + 7)(3² + 7)(9² + 7)(262² + 7)
= (9² + 7)(11² + 7)(262² + 7).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27816

27816² = (1² + 3)(15² + 3)(27² + 3)(34² + 3) = (1² + 3)(3² + 3)(4² + 3)(27² + 3)(34² + 3).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27825

27825² = (1² + 6)(3² + 6)(43² + 6)(63² + 6).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27832

27832²± 3 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27846

27846²± 5 are primes.

27846² = 775399716, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27880

27880² = (18² + 4)(26² + 4)(59² + 4) = (2² + 4)(9² + 4)(18² + 4)(59² + 4)
= (4² + 4)(8² + 4)(756² + 4).

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27889

27889 =167² is a square with nondecreasing digits.

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27908

27908²± 3 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27914

27914² = 779191396, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

27942

27942²± 5 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

27984

27984² = 783104256 is a square with different digits.

Page of Squares : First Upload April 21, 2012 ; Last Revised April 21, 2012
by Yoshio Mimura, Kobe, Japan

27986

27986²± 3 are primes.

Page of Squares : First Upload February 15, 2014 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan