The pairs of positive integers
Source: Chinese TST 2007 6th quiz P1
January 4, 2009
modular arithmeticnumber theory proposednumber theory
Problem Statement
Find all the pairs of positive integers such that a^2 \plus{} b \minus{} 1 is a power of prime number ; a^2 \plus{} b \plus{} 1 can divide b^2 \minus{} a^3 \minus{} 1, but it can't divide (a \plus{} b \minus{} 1)^2.