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k = d (a) = d (b) = d (2a + 3b), no of positive divisors

Source: 2020 Dutch IMO TST 3.1

November 22, 2020

number theorynumber of divisors

Problem Statement

For a positive number

n

, we write

d (n)

for the number of positive divisors of

n

. Determine all positive integers

k

for which exist positive integers

a

and

b

with the property

k = d (a) = d (b) = d (2a + 3b)