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Divisors and finding n

Source: Moldavian TST_1, Problem 1

March 6, 2006
number theory proposednumber theory

Problem Statement

Determine all even numbers nn, n∈Nn \in \mathbb N such that 1d1+1d2+⋯+1dk=16201003,{ \frac{1}{d_{1}}+\frac{1}{d_{2}}+ \cdots +\frac{1}{d_{k}}=\frac{1620}{1003}}, where d1,d2,…,dkd_1, d_2, \ldots, d_k are all different divisors of nn.
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