ISL Shortlist 1997 - Arithmetic progression
Source: IMO Shortlist 1997, Q15, Romanian TST 1998
August 31, 2003
number theorymodular arithmeticPerfect Squareperfect cubearithmetic sequenceIMO ShortlistRomanian TST
Problem Statement
An infinite arithmetic progression whose terms are positive integers contains the square of an integer and the cube of an integer. Show that it contains the sixth power of an integer.