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Math Help - If r,s,t are prime nos. and p,q are the positive integers ....

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    Newbie findmehere.genius's Avatar
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    If r,s,t are prime nos. and p,q are the positive integers ....

    A liitle help!

    If r,s,t are prime nos. and p,q are the positive integers such that the LCM of p,q is (r^2)*(t^4)*(s^2) then find the number of ordered pair (p,q)...just wanted to verify the answer....
    Last edited by mr fantastic; March 1st 2011 at 11:52 AM. Reason: Re-titled.
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    Quote Originally Posted by findmehere.genius View Post
    A liitle help!

    If r,s,t are prime nos. and p,q are the positive integers such that the LCM of p,q is (r^2)*(t^4)*(s^2) then find the number of ordered pair (p,q)...just wanted to verify the answer....

    If P:=\{p\in\mathbb{N}\;;\;p\,\,a\,\,prime\} , and if \displaystyle{n=\prod\limits_{p\in P}}p^{a_p}\,,\,\,m=\prod\limits_{p\in P}p^{b_p}} , with

    a_p=b_p=0 for all but a finite number of primes, then LCM(n,m)=\prod\limits_{p\in P}p^{max(a_p,b_p)} .

    Thus in our case, either p or q will have to be divided by each of those primes to the corresp. power.

    For example, (r^2t^4s^2,1),\, (rt^3s^2,r^2t^4),\, (rt^3s^2,r^2t^4s) are some of the

    wanted pairs. Now you find them all.

    Tonio
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    Newbie findmehere.genius's Avatar
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    thanks tonio, it was exactly what we( I and a friend) were trying, answer gives us 225...!
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