let n=p1^r1p2^r2p3^r3...pk^rk where p1,p2,..pk are distinct primes and each ri>=0. prove that n is a perfect square if and only if each ri is even.

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- Sep 4th 2012, 01:55 PM #1

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- Sep 4th 2012, 02:49 PM #2
## Re: need a solutiuon for this as soon as possible.

Replace $\displaystyle r_k=2m_k$ it is too obvious that resulting number n is perfect square because it is a multiple of perfect squares.

However, if even one of the powers r be an odd number then n = composed of multiple of one or more prime numbers with power =1 that cannot be perfect square!