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Math Help - little help please

  1. #1
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    little help please

    Assume we have integers a, b, and c such that c =ab and gcd(a,b)=1. Show that c is a perfect square if and only if a and b are perfect squares.
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    Quote Originally Posted by padsinseven View Post
    Assume we have integers a, b, and c such that c =ab and gcd(a,b)=1. Show that c is a perfect square if and only if a and b are perfect squares.
    This can be done using the prime factorization of the numbers a and b. There might be a faster way, though.

    -Dan
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    Little more information

    Could you elaborate please?
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    Quote Originally Posted by padsinseven View Post
    Could you elaborate please?
    Let a=p_1^{a_1}...p_n^{a_n} and b=q_1^{b_1}...q_m^{a_m} so if ab = p_1^{a_1}...q_m^{b_m} is a square it means all exponents a_1,a_2,...,b_m are even so a and b have even exponents and so are squares.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    Let a=p_1^{a_1}...p_n^{a_n} and b=q_1^{b_1}...q_m^{a_m} so if ab = p_1^{a_1}...q_m^{b_m} is a square it means all exponents a_1,a_2,...,b_m are even so a and b have even exponents and so are squares.
    That wasn't so long a proof. Though I'm sure I wouldn't have been able to state it so succinctly.

    -Dan
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    Quote Originally Posted by topsquark View Post
    That wasn't so long a proof. Though I'm sure I wouldn't have been able to state it so succinctly.
    Thank you for the +rep+ points my reputation explode up so fast.
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  7. #7
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    Quote Originally Posted by ThePerfectHacker View Post
    Thank you for the +rep+ points my reputation explode up so fast.
    Really? How many points did you jump? (I didn't know my Kung Foo was that strong. )

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    Quote Originally Posted by topsquark View Post
    Really? How many points did you jump? (I didn't know my Kung Foo was that strong.
    I am not even sure I think something like 50.
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    Quote Originally Posted by ThePerfectHacker View Post
    I am not even sure I think something like 50.
    Criminy! If I can do that, imagine what Jhevon could do.

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