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Number of divisors between k and prime p

Source: Japan Mathematical Olympiad Finals 2016 Q1

April 10, 2016

number theoryprime numbers

Problem Statement

Let

p

be an odd prime number. For positive integer

k

satisfying

1\le k\le p-1

, the number of divisors of

kp+1

between

k

and

p

exclusive is

a_k

. Find the value of

a_1+a_2+\ldots + a_{p-1}