Solving Diophantine Equations Involving GCD and Divisibility

[bronxbombas]

Homework Statement

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

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.

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.

 

[bronxbombas]

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]

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?