---

42021

42021² = 88³ + 89³ + 90³ + 91³ + 92³ + ... + 290³.

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

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42025

42025 = (4³ + 2³ + 0³ + 2³ + 5³)².

42025 = 205², and 4 = 2², 2025 = 45².

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

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42028

42028² = (4² + 3)(47² + 3)(205² + 3).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42054

42054² = (16² + 2)(18² + 2)(145² + 2).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42063

42063²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42066

42066² = (1² + 2)(4² + 2)(6² + 2)(13² + 2)(71² + 2) = (2² + 2)(5² + 2)(11² + 2)(298² + 2).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42070

42070² = 8576² + 8577² + 8578² + 8579² + ... + 8599².

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

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42150

42150² = (1² + 9)(13329² + 9).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42166

42166² = 1777971556, 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

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42182

42182²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

---

42183

42183² = (34² + 5)(1238² + 5).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42194

42194² = (12² + 2)(3492² + 2).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42210

42210² = (5² + 5)(10² + 5)(14² + 5)(53² + 5).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42240

42240² = (3² - 1)(7² - 1)(9² - 1)(241² - 1) = (3² - 1)(11² - 1)(21² - 1)(65² - 1)
= (3² - 1)(21² - 1)(23² - 1)(31² - 1) = (21² - 1)(31² - 1)(65² - 1).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42250

42250² = (5² + 1)(8² + 1)(18² + 1)(57² + 1)
= (1² + 4)(3² + 4)(11² + 4)(16² + 4)(29² + 4) = (3² + 4)(11² + 4)(29² + 4)(36² + 4).

Page of Squares : First Upload November 9, 2013 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42276

42276² = (3² + 3)(57² + 3)(214² + 3).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42327

42327²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42336

210² + 42336 = 294², 210² - 42336 = 42².

42336² = (8² - 1)(55² - 1)(97² - 1).

Page of Squares : First Upload July 28, 2012 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42340

42340²± 3 are primes.

42340² = (4² + 4)(5² + 4)(19² + 4)(92² + 4) = (19² + 4)(24² + 4)(92² + 4).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42348

42348²± 5 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

---

42350

42350² = (1² + 6)(2² + 6)(4² + 6)(29² + 6)(37² + 6) = (1² + 6)(4² + 6)(37² + 6)(92² + 6)
= (2² + 6)(4² + 6)(7² + 6)(13² + 6)(29² + 6) = (2² + 6)(7² + 6)(29² + 6)(62² + 6)
= (4² + 6)(7² + 6)(13² + 6)(92² + 6) = (4² + 6)(8² + 6)(29² + 6)(37² + 6)
= (7² + 6)(62² + 6)(92² + 6).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42372

37³ + 42372 = 305², 37³ - 42372 = 91².

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

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42420

42420²= 1106 x 1107 + 1107 x 1108 + 1108 x 1109 + 1109 x 1110 + ... + 1889 x 1890.

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

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42421

(42421² + 9) = (2² + 9)(4² + 9)(8² + 9)(14² + 9)(19² + 9).

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

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42424

42424² = 1799795776, 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

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42426

42426²± 5 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42429

42429²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42436

42436 = 206², a zigzag square.

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

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42458

42458²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42483

42483²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42500

42500² = (1² + 9)(5² + 9)(29² + 9)(79² + 9).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42504

485² + 42504 = 527², 485² - 42504 = 439².

42504² = (22² - 1)(43² - 1)(45² - 1).

Page of Squares : First Upload July 28, 2012 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42510

42510² = (2² + 9)(9² + 9)(10² + 9)(119² + 9) = (2² + 9)(10² + 9)(11² + 9)(99² + 9)
= (2² + 9)(99² + 9)(119² + 9) = (10² + 9)(41² + 9)(99² + 9).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42519

42519²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42524

42524²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

---

42525

42525² = (2² - 1)(4² - 1)(26² - 1)(244² - 1).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42532

42532² = (2² + 3)(5² + 3)(37² + 3)(82² + 3).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42536

42536²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42537

42537²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42596

42596²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42630

42630² = (1² + 6)(2² + 6)(9² + 6)(20² + 6)(27² + 6) = (1² + 6)(3² + 6)(9² + 6)(20² + 6)(22² + 6)
= (1² + 6)(6² + 6)(9² + 6)(13² + 6)(20² + 6) = (1² + 6)(9² + 6)(22² + 6)(78² + 6)
= (2² + 6)(6² + 6)(9² + 6)(223² + 6) = (8² + 6)(9² + 6)(20² + 6)(27² + 6)
= (9² + 6)(38² + 6)(120² + 6) = (20² + 6)(27² + 6)(78² + 6).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42636

42636² = (3² + 8)(5² + 8)(14² + 8)(126² + 8) = (3² + 8)(6² + 8)(31² + 8)(50² + 8)
= (3² + 8)(82² + 8)(126² + 8).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42640

42640² = (1² + 4)(2² + 4)(3² + 4)(4² + 4)(18² + 4)(23² + 4)
= (1² + 4)(2² + 4)(16² + 4)(18² + 4)(23² + 4) = (1² + 4)(4² + 4)(10² + 4)(18² + 4)(23² + 4)
= (2² + 4)(4² + 4)(23² + 4)(146² + 4) = (2² + 4)(10² + 4)(23² + 4)(64² + 4)
= (2² + 4)(18² + 4)(23² + 4)(36² + 4) = (3² + 4)(4² + 4)(6² + 4)(18² + 4)(23² + 4)
= (3² + 4)(4² + 4)(18² + 4)(146² + 4) = (3² + 4)(10² + 4)(18² + 4)(64² + 4)
= (6² + 4)(16² + 4)(18² + 4)(23² + 4) = (16² + 4)(18² + 4)(146² + 4).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42642

42642²± 5 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42645

42645²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42650

42650²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42688

42688² = (1² + 7)(4² + 7)(3147² + 7) = (1² + 7)(4² + 7)(43² + 7)(73² + 7)
= (15² + 7)(43² + 7)(65² + 7).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42700

42700²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

---

42728

42728²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42744

42744² = 1827049536, a square with different digits.

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

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42747

42747²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42756

42756²± 5 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42768

42768² = (1² + 8)(2² + 8)(4² + 8)(5² + 8)(8² + 8)(17² + 8)
= (1² + 8)(2² + 8)(5² + 8)(16² + 8)(44² + 8) = (1² + 8)(2² + 8)(8² + 8)(17² + 8)(28² + 8)
= (1² + 8)(4² + 8)(10² + 8)(16² + 8)(17² + 8) = (1² + 8)(4² + 8)(10² + 8)(280² + 8)
= (1² + 8)(5² + 8)(6² + 8)(8² + 8)(44² + 8) = (1² + 8)(5² + 8)(8² + 8)(10² + 8)(28² + 8)
= (1² + 8)(8² + 8)(38² + 8)(44² + 8) = (2² + 8)(16² + 8)(17² + 8)(44² + 8)
= (2² + 8)(44² + 8)(280² + 8) = (4² + 8)(5² + 8)(8² + 8)(10² + 8)(17² + 8)
= (5² + 8)(10² + 8)(16² + 8)(44² + 8) = (6² + 8)(8² + 8)(17² + 8)(44² + 8)
= (8² + 8)(10² + 8)(17² + 8)(28² + 8).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42807

42807²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42840

613² + 42840 = 647², 613² - 42840 = 577².

42840² = (2² - 1)(3² - 1)(8² - 1)(16² - 1)(69² - 1) = (2² - 1)(3² - 1)(11² - 1)(16² - 1)(50² - 1)
= (2² - 1)(5² - 1)(50² - 1)(101² - 1) = (2² - 1)(6² - 1)(8² - 1)(16² - 1)(33² - 1)
= (2² - 1)(16² - 1)(31² - 1)(50² - 1) = (3² - 1)(4² - 1)(5² - 1)(16² - 1)(50² - 1)
= (3² - 1)(16² - 1)(19² - 1)(50² - 1) = (5² - 1)(8² - 1)(16² - 1)(69² - 1)
= (5² - 1)(11² - 1)(16² - 1)(50² - 1) = (6² - 1)(13² - 1)(16² - 1)(35² - 1)
= (26² - 1)(33² - 1)(50² - 1).

Page of Squares : First Upload July 28, 2012 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42849

42849 = 207², a zigzag square.

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

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42874

42874²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42918

42918² = 2277² + 2278² + 2279² + 2280² + ... + 2587².

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

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42920

42920² = (1² + 4)(82² + 4)(234² + 4) = (5² + 4)(34² + 4)(234² + 4).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42945

42945²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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42950

42950²= 1396 x 1397 + 1397 x 1398 + 1398 x 1399 + 1399 x 1400 + ... + 2020 x 2021.

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

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42971

42971² = 3⁵ + 49⁵ + 69⁵.

Page of Squares : First Upload September 18, 2013 ; Last Revised September 18, 2013
by Yoshio Mimura, Kobe, Japan

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42988

42988²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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