# Math Help - need a solutiuon for this as soon as possible.

1. ## need a solutiuon for this as soon as possible.

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.

2. ## Re: need a solutiuon for this as soon as possible.

Originally Posted by lenin1234007
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.
Replace $r_k=2m_k$ 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!