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Diophantine Equations/GCD

1. Homework Statement
Suppose that gcd(a,b)=1 and that a|n and b|n. Prove that ab|n.


2. Homework Equations
Since we know that gcd(a,b)=1, we can say that ax+by=1 for some x,y as elements of the integer set.


3. The Attempt at a Solution
My professor said I should multiply the entire equation by n, but I still can't figure it out. Any help would be appreciated. Thanks in advance.
 

Answers and Replies

I also have another problem that takes priority over this one if anybody can help.

Prove that (2n)!/(2^n*n!) is an odd number when n is a nonnegative integer.
 
morphism
Science Advisor
Homework Helper
2,013
4
If you multiply the equation by n, you get n=nax+nby. Now use the fact that both a & b divide n.

For your second problem, have you tried expanding (2n)!/(2^n*n!) out?
 

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