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 Factorial and a Square (Posted on 2008-02-23)
If a and p are positive integers, then solve for (a,p):
a2=p!

 Submitted by Praneeth Rating: 2.0000 (4 votes) Solution: (Hide) In prime factorization form of p!, every power of prime should be even. For p>1, there exists at least a prime between p/2 and p(including p). So, there exists a prime whose power is 1 (This is concluded using the formula). So, for p>1, no factorial can be a perfect square. The only solution is a=1 and p=1 in positive integers.

 Subject Author Date Solution K Sengupta 2008-02-26 05:29:42 WHY 4 TIMES?? Ady TZIDON 2008-02-25 05:36:26 a trivial remark Ady TZIDON 2008-02-25 05:03:58 a trivial remark Ady TZIDON 2008-02-25 05:03:46 a trivial remark Ady TZIDON 2008-02-25 05:03:41 a trivial remark Ady TZIDON 2008-02-25 05:03:39 easy, when you know how. FrankM 2008-02-24 10:21:29 re: No Subject Charlie 2008-02-23 14:54:44 No Subject Dej Mar 2008-02-23 13:14:56

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