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

  1. #1
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    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.
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  2. #2
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    Lightbulb Re: need a solutiuon for this as soon as possible.

    Quote Originally Posted by lenin1234007 View Post
    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!
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