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Find n if d13+d14+d15=n,(d5+1)^3=d15+1 - OIMU 1998 Problem 3

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September 12, 2010
number theory proposednumber theory

Problem Statement

The positive divisors of a positive integer nn are written in increasing order starting with 1. 1=d1<d2<d3<⋯<n1=d_1<d_2<d_3<\cdots<n Find nn if it is known that: i.  n=d13+d14+d15\, n=d_{13}+d_{14}+d_{15} ii.  (d5+1)3=d15+1\,(d_5+1)^3=d_{15}+1
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