MathDB

4

Part of 2013 Benelux

Problems(1)

Integers g for which all primes divide some g^n-n

Source: Benelux MO 2013 Q4

4/29/2013
a) Find all positive integers gg with the following property: for each odd prime number pp there exists a positive integer nn such that pp divides the two integers g^n - n \text{ and }  g^{n+1} - (n + 1). b) Find all positive integers gg with the following property: for each odd prime number pp there exists a positive integer nn such that pp divides the two integers g^n - n^2 \text{ and }g^{n+1} - (n + 1)^2.
modular arithmeticquadraticsnumber theoryDiophantine equationnumber theory unsolved