MathDB
increasing sequence

Source: Iran second round 2011

April 28, 2011
inductionnumber theory proposednumber theory

Problem Statement

Find all increasing sequences a1,a2,a3,...a_1,a_2,a_3,... of natural numbers such that for each i,j∈Ni,j\in \mathbb N, number of the divisors of i+ji+j and ai+aja_i+a_j is equal. (an increasing sequence is a sequence that if i≤ji\le j, then ai≤aja_i\le a_j.)
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