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Primes don't exceed 2004

Source: China Team Selection Test 2004, Day 2, Problem 2

October 14, 2005
LaTeXnumber theory unsolvednumber theory

Problem Statement

Let p1,p2,…,p25p_1, p_2, \ldots, p_{25} are primes which don’t exceed 2004. Find the largest integer TT such that every positive integer ≤T\leq T can be expressed as sums of distinct divisors of (p1⋅p2⋅…⋅p25)2004.(p_1\cdot p_2 \cdot \ldots \cdot p_{25})^{2004}.
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