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Factorial and a Square (Posted on 2008-02-23) Difficulty: 2 of 5
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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionK Sengupta2008-02-26 05:29:42
WHY 4 TIMES??Ady TZIDON2008-02-25 05:36:26
Some Thoughtsa trivial remarkAdy TZIDON2008-02-25 05:03:58
Some Thoughtsa trivial remarkAdy TZIDON2008-02-25 05:03:46
Some Thoughtsa trivial remarkAdy TZIDON2008-02-25 05:03:41
Some Thoughtsa trivial remarkAdy TZIDON2008-02-25 05:03:39
Solutioneasy, when you know how.FrankM2008-02-24 10:21:29
re: No SubjectCharlie2008-02-23 14:54:44
SolutionNo SubjectDej Mar2008-02-23 13:14:56
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