Maths Olympiad Prep

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Number theory Difficulty 5.7 AIME, harder Prove it

34. Let n,a,bn, a, b be positive integers. Prove:
n!bn1a(a+b)(a+(n1)b).n! \mid b^{n-1} a(a+b) \cdots(a+(n-1) b) .

Solution

34. Using the method of problem 1 in Exercise Five, divide into two cases pb,pbp \mid b, p \nmid b and apply problem 2 of the second part of Exercise Four.

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