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This document describes 3 problems for a math contest round: 1) Prove that if a prime p divides x, the equation x^2 - 1 = y^p has no positive integer solutions for y. 2) Find the number of positive integers n between 2^k and 2^(k+1) where the sequence a_n = 0, with a_1 = 0 and a_n defined recursively. 3) Given 3 pairwise disjoint circles, prove that the lines connecting the midpoints of internal tangents between each pair of circles are concurrent.
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