IMO ShortList 2001, number theory problem 3
Source: IMO ShortList 2001, number theory problem 3
September 30, 2004
modular arithmeticIMO Shortlistnumber theoryInteger sequencerecurrence relation
Problem Statement
Let a_1 \equal{} 11^{11}, \, a_2 \equal{} 12^{12}, \, a_3 \equal{} 13^{13}, and a_n \equal{} |a_{n \minus{} 1} \minus{} a_{n \minus{} 2}| \plus{} |a_{n \minus{} 2} \minus{} a_{n \minus{} 3}|, n \geq 4. Determine .