Existance of a commom divisor greater than 1
Source: Moldova NMO 2002 grade 9 problem nr.5
November 2, 2008
modular arithmetic
Problem Statement
Integers satisfy the relations a_{k\plus{}1}\equal{}a_k^3\plus{}a_k^2\plus{}a_k\plus{}2 for k\equal{}1,2,...,8. Prove that among these numbers there exist three with a common divisor greater than .