Squares:60000s

60000

10⁵ + 60000 = 400², 10⁵ - 60000 = 200²,
250² + 60000 = 350², 250² - 60000 = 50².

Page of Squares : First Upload September 29, 2012 ; Last Revised September 29, 2012
by Yoshio Mimura, Kobe, Japan

60030

60030² = (1² + 5)(15² + 5)(16² + 5)(100² + 5) = (1² + 5)(100² + 5)(245² + 5)
= (2² + 5)(13² + 5)(15² + 5)(100² + 5) = (5² + 5)(8² + 5)(13² + 5)(100² + 5)
= (15² + 5)(16² + 5)(245² + 5).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60032

60032² = (7² + 7)(21² + 7)(379² + 7).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60060

60060² = (2² - 1)(6² - 1)(7² - 1)(846² - 1) = (2² - 1)(41² - 1)(846² - 1)
= (6² - 1)(12² - 1)(25² - 1)(34² - 1) = (6² - 1)(14² - 1)(727² - 1) = (8² - 1)(9² - 1)(846² - 1)
= (71² - 1)(846² - 1).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60076

60076² = 589² + 591² + 593² + 595² + ... + 2795².

Page of Squares : First Upload September 29, 2012 ; Last Revised September 29, 2012
by Yoshio Mimura, Kobe, Japan

60102

60102²± 5 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60125

60125² = 3615015625, and 36 = 6², 15015625 = 3875².

60125² = (6² + 1)(8² + 1)(18² + 1)(68² + 1).

Page of Squares : First Upload September 29, 2012 ; Last Revised November 16, 2013
by Yoshio Mimura, Kobe, Japan

60172

60172² = (2² + 3)(35² + 3)(649² + 3).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60192

60192² = (2² - 1)(3² - 1)(5² - 1)(7² - 1)(362² - 1)
= (1² + 8)(4² + 8)(6² + 8)(12² + 8)(50² + 8) = (2² + 8)(4² + 8)(5² + 8)(6² + 8)(7² + 8)(12² + 8)
= (2² + 8)(4² + 8)(5² + 8)(12² + 8)(50² + 8) = (2² + 8)(4² + 8)(7² + 8)(12² + 8)(38² + 8)
= (2² + 8)(4² + 8)(28² + 8)(126² + 8) = (2² + 8)(6² + 8)(7² + 8)(12² + 8)(28² + 8)
= (2² + 8)(8² + 8)(16² + 8)(126² + 8) = (2² + 8)(12² + 8)(28² + 8)(50² + 8)
= (4² + 8)(5² + 8)(6² + 8)(12² + 8)(26² + 8) = (4² + 8)(12² + 8)(26² + 8)(38² + 8)
= (6² + 8)(12² + 8)(26² + 8)(28² + 8).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60206

60206²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60207

60207² = 7² + 8² + 9² + ... + 2215².

Page of Squares : First Upload September 29, 2012 ; Last Revised September 29, 2012
by Yoshio Mimura, Kobe, Japan

60232

60232²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60248

60248² = 943 x 944 + 944 x 945 + 945 x 946 + ... + 2271 x 2272.

Page of Squares : First Upload September 29, 2012 ; Last Revised September 29, 2012
by Yoshio Mimura, Kobe, Japan

60265

The quadratic polynomial 60265X² - 329290X + 1108081 takes the values 916², 831², 814², 869², 984², 1141² at X = 1, 2,..., 6.

Page of Squares : First Upload September 29, 2012 ; Last Revised September 29, 2012
by Yoshio Mimura, Kobe, Japan

60270

60270² = (1² + 5)(6² + 5)(10² + 5)(375² + 5) = (4² + 5)(5² + 5)(6² + 5)(375² + 5)
= (4² + 5)(35² + 5)(375² + 5) = (6² + 5)(25² + 5)(375² + 5).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60306

60306² = 102 x 103 + 103 x 104 + 104 x 105 + ... + 2217 x 2218,
60306² = 4354² + 4355² + 4356² + ... + 4537².

Page of Squares : First Upload September 29, 2012 ; Last Revised September 29, 2012
by Yoshio Mimura, Kobe, Japan

60320

60320² = (2² + 4)(3² + 4)(4² + 4)(5² + 4)(10² + 4)(24² + 4)
= (2² + 4)(3² + 4)(4² + 4)(16² + 4)(82² + 4) = (2² + 4)(4² + 4)(5² + 4)(6² + 4)(140² + 4)
= (2² + 4)(4² + 4)(24² + 4)(198² + 4) = (2² + 4)(4² + 4)(34² + 4)(140² + 4)
= (2² + 4)(5² + 4)(10² + 4)(16² + 4)(24² + 4) = (2² + 4)(6² + 4)(24² + 4)(140² + 4)
= (4² + 4)(10² + 4)(16² + 4)(82² + 4).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60358

60358²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60405

(60405² + 3) = (1² + 3)(2² + 3)(4² + 3)(6² + 3)(16² + 3)(26² + 3).

Page of Squares : First Upload September 29, 2012 ; Last Revised September 29, 2012
by Yoshio Mimura, Kobe, Japan

60434

60434²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60447

60447²± 2 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60448

60448²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60458

60458²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60466

60466²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60480

60480² = (2² - 1)(3² - 1)(4² - 1)(8² - 1)(13² - 1)(31² - 1)
= (2² - 1)(3² - 1)(5² - 1)(8² - 1)(11² - 1)(29² - 1) = (2² - 1)(3² - 1)(5² - 1)(26² - 1)(97² - 1)
= (2² - 1)(3² - 1)(6² - 1)(13² - 1)(161² - 1) = (2² - 1)(4² - 1)(5² - 1)(19² - 1)(97² - 1)
= (2² - 1)(4² - 1)(6² - 1)(7² - 1)(13² - 1)(17² - 1)
= (2² - 1)(4² - 1)(7² - 1)(8² - 1)(11² - 1)(15² - 1) = (2² - 1)(4² - 1)(8² - 1)(9² - 1)(127² - 1)
= (2² - 1)(4² - 1)(11² - 1)(15² - 1)(55² - 1) = (2² - 1)(4² - 1)(13² - 1)(17² - 1)(41² - 1)
= (2² - 1)(4² - 1)(71² - 1)(127² - 1) = (2² - 1)(5² - 1)(6² - 1)(17² - 1)(71² - 1)
= (2² - 1)(5² - 1)(6² - 1)(8² - 1)(9² - 1)(17² - 1) = (2² - 1)(5² - 1)(8² - 1)(29² - 1)(31² - 1)
= (2² - 1)(5² - 1)(13² - 1)(19² - 1)(29² - 1) = (2² - 1)(7² - 1)(8² - 1)(13² - 1)(49² - 1)
= (2² - 1)(7² - 1)(8² - 1)(9² - 1)(71² - 1) = (2² - 1)(7² - 1)(13² - 1)(15² - 1)(26² - 1)
= (2² - 1)(8² - 1)(9² - 1)(17² - 1)(29² - 1) = (2² - 1)(8² - 1)(11² - 1)(13² - 1)(31² - 1)
= (2² - 1)(9² - 1)(55² - 1)(71² - 1) = (2² - 1)(13² - 1)(49² - 1)(55² - 1)
= (2² - 1)(17² - 1)(29² - 1)(71² - 1) = (3² - 1)(4² - 1)(5² - 1)(8² - 1)(11² - 1)(13² - 1)
= (3² - 1)(4² - 1)(6² - 1)(7² - 1)(8² - 1)(17² - 1) = (3² - 1)(4² - 1)(6² - 1)(17² - 1)(55² - 1)
= (3² - 1)(4² - 1)(8² - 1)(17² - 1)(41² - 1) = (3² - 1)(5² - 1)(8² - 1)(19² - 1)(29² - 1)
= (3² - 1)(7² - 1)(8² - 1)(15² - 1)(26² - 1) = (3² - 1)(8² - 1)(11² - 1)(13² - 1)(19² - 1)
= (3² - 1)(8² - 1)(49² - 1)(55² - 1) = (3² - 1)(15² - 1)(26² - 1)(55² - 1)
= (4² - 1)(5² - 1)(8² - 1)(13² - 1)(31² - 1) = (4² - 1)(7² - 1)(8² - 1)(15² - 1)(19² - 1)
= (4² - 1)(7² - 1)(41² - 1)(55² - 1) = (4² - 1)(8² - 1)(9² - 1)(13² - 1)(17² - 1)
= (4² - 1)(13² - 1)(17² - 1)(71² - 1) = (4² - 1)(15² - 1)(19² - 1)(55² - 1)
= (4² - 1)(97² - 1)(161² - 1) = (5² - 1)(6² - 1)(13² - 1)(161² - 1)
= (6² - 1)(7² - 1)(8² - 1)(11² - 1)(17² - 1) = (6² - 1)(11² - 1)(17² - 1)(55² - 1)
= (8² - 1)(11² - 1)(17² - 1)(41² - 1) = (8² - 1)(13² - 1)(19² - 1)(31² - 1)
= (8² - 1)(17² - 1)(449² - 1) = (13² - 1)(29² - 1)(161² - 1).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60504

60504² = (1² + 3)(3² + 3)(8733² + 3).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60507

60507²± 2 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60516

60516 = 246², a zigzag square.

60516² = (19² + 8)(22² + 8)(142² + 8).

Page of Squares : First Upload September 29, 2012 ; Last Revised September 29, 2012
by Yoshio Mimura, Kobe, Japan

60520

60520² = (1² + 4)(110² + 4)(246² + 4) = (2² + 4)(9² + 4)(21² + 4)(110² + 4)
= (21² + 4)(26² + 4)(110² + 4).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60522

60522² = (15² + 6)(16² + 6)(246² + 6).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60526

60526²± 3 are primes.

60526² = 3663396676, and 3663396 = 1914, 676 = 26.

Page of Squares : First Upload September 29, 2012 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60528

60528² = (1² + 3)(3² + 3)(71² + 3)(123² + 3).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60534

60534² = (2² + 2)(5² + 2)(4756² + 2) = (2² + 2)(13² + 2)(23² + 2)(82² + 2)
= (5² + 2)(6² + 2)(23² + 2)(82² + 2) = (23² + 2)(32² + 2)(82² + 2).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60536

60536²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60544

60544² = (2² + 7)(3² + 7)(5² + 7)(6² + 7)(123² + 7) = (2² + 7)(3² + 7)(37² + 7)(123² + 7)
= (2² + 7)(5² + 7)(6² + 7)(13² + 7)(37² + 7) = (2² + 7)(6² + 7)(37² + 7)(75² + 7)
= (5² + 7)(6² + 7)(13² + 7)(123² + 7) = (6² + 7)(75² + 7)(123² + 7) = (13² + 7)(37² + 7)(123² + 7).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60555

60555²± 2 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60564

60564² = (1² + 3)(2² + 3)(10² + 3)(12² + 3)(93² + 3) = (5² + 3)(10² + 3)(12² + 3)(93² + 3).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60573

60573²± 2 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60588

60588² = (1² + 2)(2² + 2)(3² + 2)(4² + 2)(5² + 2)(8² + 2)(24² + 2)
= (1² + 2)(2² + 2)(3² + 2)(4² + 2)(7² + 2)(10² + 2)(14² + 2)
= (1² + 2)(2² + 2)(3² + 2)(8² + 2)(22² + 2)(24² + 2)
= (1² + 2)(2² + 2)(4² + 2)(7² + 2)(8² + 2)(58² + 2)
= (1² + 2)(2² + 2)(4² + 2)(8² + 2)(10² + 2)(41² + 2) = (1² + 2)(2² + 2)(4² + 2)(24² + 2)(140² + 2)
= (1² + 2)(2² + 2)(5² + 2)(8² + 2)(14² + 2)(24² + 2)
= (1² + 2)(4² + 2)(7² + 2)(8² + 2)(10² + 2)(14² + 2) = (1² + 2)(4² + 2)(10² + 2)(14² + 2)(58² + 2)
= (2² + 2)(3² + 2)(4² + 2)(5² + 2)(14² + 2)(24² + 2) = (2² + 2)(3² + 2)(14² + 2)(22² + 2)(24² + 2)
= (2² + 2)(4² + 2)(7² + 2)(14² + 2)(58² + 2) = (2² + 2)(4² + 2)(10² + 2)(14² + 2)(41² + 2)
= (2² + 2)(5² + 2)(8² + 2)(10² + 2)(58² + 2) = (8² + 2)(14² + 2)(22² + 2)(24² + 2)
= (1² + 8)(2² + 8)(3² + 8)(5² + 8)(6² + 8)(37² + 8)
= (1² + 8)(2² + 8)(3² + 8)(5² + 8)(14² + 8)(17² + 8)
= (1² + 8)(2² + 8)(3² + 8)(17² + 8)(82² + 8) = (1² + 8)(2² + 8)(3² + 8)(37² + 8)(38² + 8)
= (1² + 8)(2² + 8)(3² + 8)(1414² + 8) = (1² + 8)(2² + 8)(5² + 8)(14² + 8)(71² + 8)
= (1² + 8)(2² + 8)(71² + 8)(82² + 8) = (1² + 8)(3² + 8)(5² + 8)(10² + 8)(82² + 8)
= (1² + 8)(3² + 8)(6² + 8)(10² + 8)(71² + 8) = (1² + 8)(5² + 8)(6² + 8)(14² + 8)(37² + 8)
= (1² + 8)(5² + 8)(6² + 8)(530² + 8) = (1² + 8)(6² + 8)(37² + 8)(82² + 8)
= (1² + 8)(14² + 8)(17² + 8)(82² + 8) = (1² + 8)(14² + 8)(37² + 8)(38² + 8)
= (1² + 8)(14² + 8)(1414² + 8) = (1² + 8)(38² + 8)(530² + 8)
= (2² + 8)(3² + 8)(5² + 8)(10² + 8)(71² + 8) = (2² + 8)(3² + 8)(6² + 8)(17² + 8)(37² + 8)
= (2² + 8)(5² + 8)(37² + 8)(82² + 8) = (2² + 8)(6² + 8)(37² + 8)(71² + 8)
= (2² + 8)(14² + 8)(17² + 8)(71² + 8) = (3² + 2)(4² + 2)(8² + 2)(22² + 2)(24² + 2)
= (3² + 8)(5² + 8)(6² + 8)(10² + 8)(37² + 8) = (3² + 8)(5² + 8)(10² + 8)(14² + 8)(17² + 8)
= (3² + 8)(10² + 8)(17² + 8)(82² + 8) = (3² + 8)(10² + 8)(37² + 8)(38² + 8)
= (3² + 8)(10² + 8)(1414² + 8) = (4² + 2)(5² + 2)(8² + 2)(14² + 2)(24² + 2)
= (5² + 8)(10² + 8)(14² + 8)(71² + 8) = (6² + 8)(14² + 8)(17² + 8)(37² + 8)
= (6² + 8)(17² + 8)(530² + 8) = (10² + 8)(71² + 8)(82² + 8).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60752

60752²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60753

60753²± 2 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60778

60778²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60816

60816² = (1² + 3)(2² + 3)(3² + 3)(5² + 3)(627² + 3) = (1² + 3)(5² + 3)(9² + 3)(627² + 3).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60830

60830² = (1² + 6)(2² + 6)(4² + 6)(7² + 6)(209² + 6) = (1² + 6)(28² + 6)(818² + 6)
= (2² + 6)(92² + 6)(209² + 6) = (4² + 6)(7² + 6)(8² + 6)(209² + 6) = (4² + 6)(62² + 6)(209² + 6).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60854

60854²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60858

60858² = (1² + 5)(2² + 5)(8² + 5)(31² + 5)(32² + 5) = (1² + 5)(2² + 5)(8² + 5)(997² + 5)
= (1² + 5)(4² + 5)(8² + 5)(17² + 5)(38² + 5) = (1² + 5)(4² + 5)(32² + 5)(169² + 5)
= (2² + 5)(3² + 5)(4² + 5)(31² + 5)(38² + 5) = (2² + 5)(3² + 5)(8² + 5)(17² + 5)(38² + 5)
= (2² + 5)(3² + 5)(32² + 5)(169² + 5) = (2² + 5)(4² + 5)(8² + 5)(17² + 5)(31² + 5)
= (2² + 5)(17² + 5)(31² + 5)(38² + 5) = (3² + 5)(4² + 5)(8² + 5)(11² + 5)(38² + 5)
= (3² + 5)(8² + 5)(32² + 5)(61² + 5) = (4² + 5)(11² + 5)(31² + 5)(38² + 5)
= (11² + 5)(32² + 5)(169² + 5) = (7² + 5)(8² + 5)(31² + 5)(32² + 5)
= (7² + 5)(8² + 5)(997² + 5) = (8² + 5)(11² + 5)(17² + 5)(38² + 5)
= (31² + 5)(32² + 5)(61² + 5) = (61² + 5)(997² + 5).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60879

60879² = 1029² + 1030² + 1031² + ... + 2302².

Page of Squares : First Upload September 29, 2012 ; Last Revised September 29, 2012
by Yoshio Mimura, Kobe, Japan

60891

60891²± 2 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60892

60892²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60900

60900² = (2² + 6)(3² + 6)(6² + 6)(20² + 6)(38² + 6) = (2² + 6)(6² + 6)(8² + 6)(9² + 6)(38² + 6)
= (2² + 6)(6² + 6)(38² + 6)(78² + 6) = (2² + 6)(8² + 6)(9² + 6)(12² + 6)(20² + 6)
= (2² + 6)(12² + 6)(20² + 6)(78² + 6) = (6² + 6)(12² + 6)(20² + 6)(38² + 6).

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60924

60924² = 3711733776, 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

60928

60928²± 3 are primes.

Page of Squares : First Upload March 23, 2014 ; Last Revised March 23, 2014
by Yoshio Mimura, Kobe, Japan

60973

60973² = 3807² + 3808² + 3809² + ... + 4047².

Page of Squares : First Upload September 29, 2012 ; Last Revised September 29, 2012
by Yoshio Mimura, Kobe, Japan

60984

60984² = 3719048256, a square with different digits.

Page of Squares : First Upload September 29, 2012 ; Last Revised September 29, 2012
by Yoshio Mimura, Kobe, Japan

60988

60988² = 6177² + 6178² + 6179² + ... + 6272².

Page of Squares : First Upload September 29, 2012 ; Last Revised September 29, 2012
by Yoshio Mimura, Kobe, Japan