Factorial and a Square (Posted on 2008-02-23)

	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