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Integers problem

發問:

If n and p are integer greater than 1 and if p is a factor of both n+3 and n+10, what is the value of p?

最佳解答:

p is a factor of n+3 => n+3 = p*A for some integer constant A ... (1) p is a factor of n+10 => n+10 = p*B for some integer constant B ... (2) Equation (2) minus equation (1) gives 7 = p * (B-A) = p*C for some integer constant C = B-A So p should also be a factor of 7. Since 7 only has two factors, 1 and 7, and p cannot be 1 as said in the question, p = 7.

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