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## Homework Statement

Define [tex] {x \choose n}=\frac{x(x-1)(x-2)...(x-n+1)}{n!} [/tex] for positive integer n. For what values of positive integers n and m is [tex]g(x)={{{x+1} \choose n} \choose {m}}-{{{x} \choose n} \choose {m}}[/tex] a factor of [tex]f(x)={{{x+1} \choose n} \choose {m}}[/tex]?

## Homework Equations

The idea that the roots of a polynomial must be roots of its factors perhaps.

## The Attempt at a Solution

I quickly found by brute force that m=n=1 and m=n=2 worked, but I’m not sure how to get a general result. Any help would be appreciated.

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