Squares:47000s

47040

238² + 47040 = 322², 238² - 47040 = 98².

47040² = (2² - 1)(3² - 1)(97² - 1)(99² - 1) = (3² - 1)(6² - 1)(29² - 1)(97² - 1)
= (5² - 1)(97² - 1)(99² - 1) = (6² - 1)(13² - 1)(15² - 1)(41² - 1).

Page of Squares : First Upload August 11, 2012 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47044

47044²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47060

47060² = (1² + 1)(5² + 1)(19² + 1)(343² + 1).

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

47061

47061² = (2² + 5)(4² + 5)(24² + 5)(142² + 5).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47082

47082²± 5 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47089

47089 = 217², a square with different digits.

Page of Squares : First Upload August 11, 2012 ; Last Revised August 11, 2012
by Yoshio Mimura, Kobe, Japan

47096

47096² = (14² + 7)(15² + 7)(217² + 7).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47104

47104² = (1² + 7)(3² + 7)(5² + 7)(11² + 7)(65² + 7) = (1² + 7)(4² + 7)(19² + 7)(181² + 7)
= (3² + 7)(65² + 7)(181² + 7).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47110

47110²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47122

47122² = 2220482884, a square with even digits.

Page of Squares : First Upload August 11, 2012 ; Last Revised August 11, 2012
by Yoshio Mimura, Kobe, Japan

47128

47128²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47138

47138²± 3 are primes.

47138² = (2² + 3)(16² + 3)(19² + 3)(58² + 3).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47157

47157²± 2 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47162

47162² = 2224254244, a square with 3 kinds of digita.

Page of Squares : First Upload August 11, 2012 ; Last Revised August 11, 2012
by Yoshio Mimura, Kobe, Japan

47168

47168² = 2224820224, a square with even digits.

47168² = (1² + 7)(2² + 7)(13² + 7)(379² + 7) = (2² + 7)(3² + 7)(9² + 7)(379² + 7)
= (3² + 7)(5² + 7)(23² + 7)(90² + 7) = (3² + 7)(31² + 7)(379² + 7) = (9² + 7)(13² + 7)(379² + 7).

Page of Squares : First Upload August 11, 2012 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47170

47170² = (1² + 4)(21² + 4)(1000² + 4).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47175

47175² = (18² + 9)(46² + 9)(56² + 9).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47188

47188²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47196

The sum of the cubes of the divisors of 47196 is 124550956857600 = 11160240².

Page of Squares : First Upload August 11, 2012 ; Last Revised August 11, 2012
by Yoshio Mimura, Kobe, Japan

47201

47201² = 269² + 270² + 271² + 272² + ... + 1885².

Page of Squares : First Upload August 11, 2012 ; Last Revised August 11, 2012
by Yoshio Mimura, Kobe, Japan

47202

47202² = 2228028804, a square with even digits.

Page of Squares : First Upload August 11, 2012 ; Last Revised August 11, 2012
by Yoshio Mimura, Kobe, Japan

47229

47229²± 2 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47235

47235²± 2 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47277

47277²± 2 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47338

47338² = 2240886244, a square with even digits.

Page of Squares : First Upload August 11, 2012 ; Last Revised August 11, 2012
by Yoshio Mimura, Kobe, Japan

47354

47354²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47377

47377² = 612² + 613² + 614² + 615² + ... + 1909²

Page of Squares : First Upload August 11, 2012 ; Last Revised August 11, 2012
by Yoshio Mimura, Kobe, Japan

47408

47408²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47422

47422²± 3 are primes.

47422² = 2248846084, a square with even digits.

Page of Squares : First Upload August 11, 2012 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47450

47450² = (1² + 9)(4² + 9)(3001² + 9) = (1² + 9)(8² + 9)(11² + 9)(154² + 9).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47481

47481²± 2 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47424

265² + 47424 = 343², 265² - 47424 = 151².

Page of Squares : First Upload August 11, 2012 ; Last Revised August 11, 2012
by Yoshio Mimura, Kobe, Japan

47440

47440²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47488

47488² = (1² + 7)(7² + 7)(29² + 7)(77² + 7) = (21² + 7)(29² + 7)(77² + 7).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47508

47508²± 5 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47520

366² + 47520 = 426², 366² - 47520 = 294²,
219² + 47520 = 309², 219² - 47520 = 21².

47520² = (2² - 1)(3² - 1)(4² - 1)(10² - 1)(11² - 1)(23² - 1)
= (2² - 1)(3² - 1)(4² - 1)(23² - 1)(109² - 1) = (2² - 1)(3² - 1)(5² - 1)(10² - 1)(199² - 1)
= (2² - 1)(3² - 1)(9² - 1)(10² - 1)(109² - 1) = (2² - 1)(3² - 1)(10² - 1)(11² - 1)(89² - 1)
= (2² - 1)(3² - 1)(89² - 1)(109² - 1) = (2² - 1)(4² - 1)(5² - 1)(7² - 1)(10² - 1)(21² - 1)
= (2² - 1)(4² - 1)(10² - 1)(11² - 1)(65² - 1) = (2² - 1)(4² - 1)(10² - 1)(23² - 1)(31² - 1)
= (2² - 1)(4² - 1)(65² - 1)(109² - 1) = (2² - 1)(7² - 1)(10² - 1)(19² - 1)(21² - 1)
= (2² - 1)(10² - 1)(31² - 1)(89² - 1) = (2² - 1)(11² - 1)(23² - 1)(109² - 1)
= (3² - 1)(10² - 1)(19² - 1)(89² - 1) = (3² - 1)(10² - 1)(26² - 1)(65² - 1)
= (3² - 1)(4² - 1)(5² - 1)(10² - 1)(89² - 1) = (3² - 1)(4² - 1)(9² - 1)(485² - 1)
= (3² - 1)(4² - 1)(10² - 1)(19² - 1)(23² - 1) = (4² - 1)(5² - 1)(10² - 1)(11² - 1)(23² - 1)
= (4² - 1)(5² - 1)(23² - 1)(109² - 1) = (4² - 1)(10² - 1)(19² - 1)(65² - 1)
= (5² - 1)(9² - 1)(10² - 1)(109² - 1) = (5² - 1)(10² - 1)(11² - 1)(89² - 1)
= (5² - 1)(89² - 1)(109² - 1) = (9² - 1)(11² - 1)(485² - 1)
= (10² - 1)(11² - 1)(19² - 1)(23² - 1) = (19² - 1)(23² - 1)(109² - 1).

Page of Squares : First Upload August 11, 2012 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47529

47529²± 2 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47532

47532² = (2² + 8)(3² + 8)(15² + 8)(218² + 8) = (14² + 8)(15² + 8)(218² + 8).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47538

47538² = (1² + 2)(6² + 2)(50² + 2)(89² + 2).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47554

47554²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47564

47564²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47574

47574² = (1² + 2)(2² + 2)(5² + 2)(2158² + 2) = (4² + 2)(5² + 2)(2158² + 2) = (22² + 2)(2158² + 2).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47575

47575² = (37² + 6)(1283² + 6).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47600

47600² = 2074 x 2075 + 2076 x 2077 + 2078 x 2079 + 2080 x 2081 + ... + 2822 x 2823.

Page of Squares : First Upload August 11, 2012 ; Last Revised August 11, 2012
by Yoshio Mimura, Kobe, Japan

47628

47628²± 5 are primes.

47628² = (1² + 5)(2² + 5)(3² + 5)(17² + 5)(101² + 5)
= (1² + 5)(2² + 5)(4² + 5)(7² + 5)(11² + 5)(17² + 5) = (1² + 5)(3² + 5)(4² + 5)(11² + 5)(101² + 5)
= (1² + 5)(11² + 5)(17² + 5)(101² + 5) = (3² + 5)(7² + 5)(17² + 5)(101² + 5).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47632

47632²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47633

47633² = 3117² + 3118² + 3119² + ... + 3334².

Page of Squares : First Upload August 11, 2012 ; Last Revised August 11, 2012
by Yoshio Mimura, Kobe, Japan

47643

47643²± 2 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47652

47652² = (7² + 8)(50² + 8)(126² + 8).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47672

47672, 47673, 47674, 47675, 47676 and 47677 are six consecutive integers having square factors (the 4th case).

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

47724

47724² = (22² + 8)(34² + 8)(63² + 8).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47740

47740² = (1² + 6)(2² + 6)(4² + 6)(5² + 6)(8² + 6)(26² + 6)
= (2² + 6)(4² + 6)(5² + 6)(22² + 6)(26² + 6).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47742

47742²± 5 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47744

47744²± 3 are primes.

47744² = (3² + 7)(11² + 7)(1055² + 7).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47798

47798² = 2284648804, a square with even digits.

Page of Squares : First Upload August 11, 2012 ; Last Revised August 11, 2012
by Yoshio Mimura, Kobe, Japan

47848

47848²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47850

47850² = (3² + 6)(4² + 6)(7² + 6)(9² + 6)(38² + 6) = (3² + 6)(7² + 6)(12² + 6)(136² + 6)
= (7² + 6)(9² + 6)(18² + 6)(38² + 6).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47852

47852²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47855

47855² = 1695² + 1696² + 1697² + 1698² + ... + 2272².

Page of Squares : First Upload August 11, 2012 ; Last Revised August 11, 2012
by Yoshio Mimura, Kobe, Japan

47880

221² + 47880 = 311², 221² - 47880 = 31².

47880² = (3² - 1)(4² - 1)(6² - 1)(20² - 1)(37² - 1) = (6² - 1)(11² - 1)(20² - 1)(37² - 1).

Page of Squares : First Upload August 11, 2012 ; Last Revised August 11, 2012
by Yoshio Mimura, Kobe, Japan

47886

47886²± 5 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

47961

47961 = 219², a square with different digits.

Page of Squares : First Upload August 11, 2012 ; Last Revised August 11, 2012
by Yoshio Mimura, Kobe, Japan

47970

47970² = (2² + 9)(3² + 9)(14² + 9)(219² + 9) = (14² + 9)(15² + 9)(219² + 9).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan