engleski

On a variation of a congruence of Subbarao

Here, we study positive integers n such that n*phi(n) = 2 (mod sigma(n)), where phi(n) and sigma(n) are the Euler function and the sum of divisors function of the positive integer n, respectively. We give a general ineffective result showing that there are only finitely many such n whose prime factors belong to a fixed finite set. When this finite set consists only of the two primes 2 and 3 we use continued fractions to find all such positive integers n.

Euler function; sum of divisors; Pellian equations

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