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Math Help - [SOLVED] Help With Proofs

  1. #1
    Tom.O
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    [SOLVED] Help With Proofs

    Hey, could I get receive some help with these problems, thanks.

    1) Show that p is a prime number and p divides the product ab then a divides a or b divides b.
    2) Let Tn be the highest power of 2 that divides n. Show that Tnm = Tn + Tm
    3) Let n, c, and d be three integers. Show that if d * c divides n * c then d divides n.
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  2. #2
    Member
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    Quote Originally Posted by Tom.O View Post
    Hey, could I get receive some help with these problems, thanks.

    1) Show that p is a prime number and p divides the product ab then a divides a or b divides b.
    2) Let Tn be the highest power of 2 that divides n. Show that Tnm = Tn + Tm
    3) Let n, c, and d be three integers. Show that if d * c divides n * c then d divides n.
    Do you know the Fundamental Theorem of Arithmetic? These all follow from
    it with only a little work.

    ZB
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  3. #3
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    Quote Originally Posted by Constantine11
    Do you know the Fundamental Theorem of Arithmetic? These all follow from
    it with only a little work.
    We cannot use the factorization theorem. Because the proof of it is based on proving #1. And we cannot use a result to prove a result that is used to prove it.

    Quote Originally Posted by Tom.O View Post
    1) Show that p is a prime number and p divides the product ab then a divides a or b divides b.
    If p|a then proof is complete, otherwise gcd(a,p)=1 but then p|b.
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