Integers g for which all primes divide some g^n-n
Source: Benelux MO 2013 Q4
April 29, 2013
modular arithmeticquadraticsnumber theoryDiophantine equationnumber theory unsolved
Problem Statement
a) Find all positive integers with the following property: for each odd prime number there exists a positive integer such that divides the two integers
g^n - n \text{ and } g^{n+1} - (n + 1).
b) Find all positive integers with the following property: for each odd prime number there exists a positive integer such that divides the two integers
g^n - n^2 \text{ and }g^{n+1} - (n + 1)^2.