MathDB

d(a^n-1) is at least n if a^n+1 is prime

Source: Baltic Way 1996 Q10

March 19, 2011

number theoryrelatively primenumber theory proposed

Problem Statement

Denote by

d(n)

the number of distinct positive divisors of a positive integer

n

(including

1

and

n

). Let

a>1

and

n>0

be integers such that

a^n+1

is a prime. Prove that

d(a^n-1)\ge n