MathDB

Divisors

Source: 2014 Czech & Slovak Mathematical Olympiad, Rnd. III, Cat. A

May 20, 2014

modular arithmeticnumber theory unsolvednumber theory

Problem Statement

Let be

n

a positive integer. Denote all its (positive) divisors as

1=d_1<d_2<\cdots<d_{k-1}<d_k=n

. Find all values of

n

satisfying

d_5-d_3=50

and

11d_5+8d_7=3n

.
(Day 1, 1st problem author: Matúš Harminc)