MathDB

5

Part of 2017 China National Olympiad

Problems(1)

Partition divisors into AP and GP

Source: China Mathematical Olympiad 2017 Q5

11/24/2016
Let DnD_n be the set of divisors of nn. Find all natural nn such that it is possible to split DnD_n into two disjoint sets AA and GG, both containing at least three elements each, such that the elements in AA form an arithmetic progression while the elements in GG form a geometric progression.
number theoryDivisors