---

49010

49010² = (1² + 1)(5² + 1)(8² + 1)(12² + 1)(70² + 1) = (12² + 1)(17² + 1)(239² + 1)
= (2² + 1)(3² + 1)(70² + 1)(99² + 1) = (5² + 1)(8² + 1)(12² + 1)(99² + 1)
= (5² + 1)(8² + 1)(17² + 1)(70² + 1) = (7² + 1)(70² + 1)(99² + 1)
= (1² + 4)(5² + 4)(29² + 4)(140² + 4).

Page of Squares : First Upload November 9, 2013 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

---

49013

49013² = 1581² + 1583² + 1585² + 1587² + 1589² + 1591² + ... + 2637².

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

---

49050

49050² = (4² + 9)(9² + 9)(10² + 9)(99² + 9).

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

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49060

49060²± 3 are primes.

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

---

49070

49070²± 3 are primes.

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

---

49125

49125²± 2 are primes.

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

---

49126

49126²± 3 are primes.

49126² = (1² + 6)(4² + 6)(29² + 6)(136² + 6).

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

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49140

49140² = (4² - 1)(8² - 1)(25² - 1)(64² - 1) = (7² - 1)(8² - 1)(14² - 1)(64² - 1)
= (14² - 1)(55² - 1)(64² - 1).

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

---

49170

49170² = (3² + 6)(4² + 6)(21² + 6)(128² + 6) = (18² + 6)(21² + 6)(128² + 6).

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

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49200

49200² = (2² - 1)(3² - 1)(81² - 1)(124² - 1) = (5² - 1)(81² - 1)(124² - 1).

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

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49203

49203²± 2 are primes.

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

---

49242

49242² = (1² + 5)(13² + 5)(1524² + 5).

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

---

49248

49248² = (1² + 8)(2² + 8)(4² + 8)(7² + 8)(10² + 8)(12² + 8)
= (1² + 8)(4² + 8)(10² + 8)(12² + 8)(26² + 8) = (2² + 8)(8² + 8)(26² + 8)(64² + 8)
= (2² + 8)(12² + 8)(26² + 8)(44² + 8).

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

---

49290

49290² = (3² + 6)(5² + 6)(10² + 6)(222² + 6).

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

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49277

49277² = 2428222729, a square pegged by 2.

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

---

49284

49284 = 222², a zigzag square.

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

---

49300

49300² = (1² + 1)(13² + 1)(17² + 1)(157² + 1) = (1² + 1)(2² + 1)(4² + 1)(7² + 1)(13² + 1)(41² + 1)
= (1² + 1)(3² + 1)(4² + 1)(12² + 1)(13² + 1)(17² + 1) = (1² + 1)(3² + 1)(4² + 1)(17² + 1)(157² + 1)
= (1² + 1)(3² + 1)(7² + 1)(38² + 1)(41² + 1) = (3² + 1)(4² + 1)(7² + 1)(13² + 1)(41² + 1)
= (1² + 4)(4² + 4)(5² + 4)(8² + 4)(111² + 4) = (1² + 4)(8² + 4)(24² + 4)(111² + 4).

Page of Squares : First Upload November 9, 2013 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

---

49302

49302² = (1² + 2)(2² + 2)(3² + 2)(5² + 2)(9² + 2)(74² + 2)
= (1² + 2)(2² + 2)(8² + 2)(9² + 2)(157² + 2) = (1² + 2)(2² + 2)(74² + 2)(157² + 2)
= (1² + 2)(5² + 2)(8² + 2)(9² + 2)(74² + 2) = (2² + 2)(3² + 2)(4² + 2)(9² + 2)(157² + 2)
= (2² + 2)(9² + 2)(14² + 2)(157² + 2) = (3² + 2)(4² + 2)(5² + 2)(9² + 2)(74² + 2)
= (3² + 2)(9² + 2)(22² + 2)(74² + 2) = (4² + 2)(8² + 2)(9² + 2)(157² + 2)
= (4² + 2)(74² + 2)(157² + 2) = (5² + 2)(9² + 2)(14² + 2)(74² + 2).

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

---

49306

49306² = 229² + 231² + 233² + 235² + 237² + ... + 2443².

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

---

49312

49312² = (1² + 7)(4² + 7)(23² + 7)(157² + 7) = (1² + 7)(111² + 7)(157² + 7)
= (3² + 7)(4² + 7)(23² + 7)(111² + 7) = (4² + 7)(27² + 7)(379² + 7) = (19² + 7)(23² + 7)(111² + 7).

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

---

49314

49314² = 2431870596, a square with different digits.

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

---

49353

49353² = 2435718609, a square with different digits.

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

---

49360

49360²± 3 are primes.

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

---

49414

49414²± 3 are primes.

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

---

49422

49422²± 5 are primes.

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

---

49446

49446²± 5 are primes.

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

---

49449

The quadratic polynomial 49449X² - 205062X + 432289 takes the values 526², 469², 512², 635², 802², 991² at X = 1, 2,..., 6

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

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49476

49476² = (1² + 3)(2² + 3)(4² + 3)(42² + 3)(51² + 3) = (1² + 3)(4² + 3)(11² + 3)(12² + 3)(42² + 3)
= (1² + 3)(4² + 3)(42² + 3)(135² + 3) = (2² + 3)(3² + 3)(4² + 3)(15² + 3)(82² + 3)
= (2² + 3)(4² + 3)(9² + 3)(11² + 3)(42² + 3) = (4² + 3)(5² + 3)(42² + 3)(51² + 3)
= (4² + 3)(9² + 3)(15² + 3)(82² + 3) = (23² + 3)(42² + 3)(51² + 3).

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

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49514

49514²± 3 are primes.

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

---

49572

49572² = (1² + 2)(2² + 2)(4² + 2)(5² + 2)(22² + 2)(24² + 2).

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

---

49574

49574²± 3 are primes.

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

---

49610

49610²± 3 are primes.

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

---

49644

49644²± 5 are primes.

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

---

49658

49658²± 3 are primes.

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

---

49659

49659²± 2 are primes.

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

---

49685

49665² = 144³ + 145³ + 146³ + 147³ + 148³ + ... + 318³.

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

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49686

49686² = (1² + 3)(2² + 3)(6² + 3)(12² + 3)(124² + 3) = (5² + 3)(6² + 3)(12² + 3)(124² + 3)
= (12² + 3)(33² + 3)(124² + 3).

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

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49704

49704² = (1² + 3)(3² + 3)(4² + 3)(18² + 3)(91² + 3) = (1² + 3)(15² + 3)(18² + 3)(91² + 3).

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

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49707

49707²± 2 are primes.

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

---

49720

49720²= 354 x 355 + 355 x 356 + 356 x 357 +...+ 1953 x 1954.

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

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49725

49725² = (2² + 9)(4² + 9)(24² + 9)(114² + 9) = (2² + 9)(12² + 9)(24² + 9)(46² + 9)
= (4² + 9)(12² + 9)(804² + 9).

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

---

49729

49729 = 223², and 49 = 7², 729 = 27².

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

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49737

49737²± 2 are primes.

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

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49743

49743²± 2 are primes.

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

---

49756

49756² = (1² + 3)(2² + 3)(9403² + 3) = (5² + 3)(9403² + 3).

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

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49758

49758²± 5 are primes.

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

---

49761

49761² = (1² + 8)(7² + 8)(2197² + 8).

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

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49826

49826²± 3 are primes.

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

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49848

49848² = (1² + 3)(3² + 3)(8² + 3)(879² + 3).

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

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49851

49851² = 809² + 811² + 813² + 815² + 817² + ... + 2489².

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

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49896

255² + 49896 = 339², 255² - 49896 = 123².

49896² = (8² - 1)(13² - 1)(485² - 1).

Page of Squares : First Upload August 18, 2012 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

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49910

49910² = 2725² + 2727² + 2729² + 2731² + 2733² + ... + 3275².

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

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49920

49920² = (2² - 1)(3² - 1)(79² - 1)(129² - 1) = (2² - 1)(9² - 1)(25² - 1)(129² - 1)
= (3² - 1)(9² - 1)(25² - 1)(79² - 1) = (5² - 1)(79² - 1)(129² - 1).

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

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49932

49932² = (1² + 2)(2² + 2)(4² + 2)(6² + 2)(450² + 2) = (1² + 2)(2² + 2)(6² + 2)(12² + 2)(158² + 2)
= (4² + 2)(6² + 2)(12² + 2)(158² + 2).

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

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49938

49938² = (1² + 5)(129² + 5)(158² + 5) = (3² + 5)(6² + 5)(13² + 5)(158² + 5)
= (3² + 5)(6² + 5)(16² + 5)(129² + 5) = (4² + 5)(6² + 5)(13² + 5)(129² + 5) = (71² + 5)(703² + 5).

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

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49948

49948²± 3 are primes.

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

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49950

49950² = (1² + 9)(3² + 9)(18² + 9)(204² + 9) = (1² + 9)(6² + 9)(18² + 9)(129² + 9)
= (3² + 9)(4² + 9)(6² + 9)(18² + 9)(19² + 9) = (3² + 9)(4² + 9)(6² + 9)(351² + 9)
= (3² + 9)(4² + 9)(18² + 9)(129² + 9) = (6² + 9)(18² + 9)(19² + 9)(21² + 9)
= (6² + 9)(21² + 9)(351² + 9) = (18² + 9)(21² + 9)(129² + 9).

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

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49959

49959² = 714² + 715² + 716² + 717² + ... + 1987².

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

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49964

49964² = 2496401296, 24964 = 158² and 1296 = 36².

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

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49973

49973² = 687² + 688² + 689² + 690² + ... + 1984².

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

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49980

49980² = (6² - 1)(50² - 1)(169² - 1).

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

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49984

49984² = (2² + 7)(3² + 7)(5² + 7)(8² + 7)(79² + 7) = (3² + 7)(5² + 7)(2209² + 7)
= (3² + 7)(8² + 7)(1483² + 7) = (5² + 7)(8² + 7)(13² + 7)(79² + 7) = (8² + 7)(75² + 7)(79² + 7).

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

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