Divisibility Of Power Differences
Number Theory
Level
4
Let \( a \) and \( b \) be positive integers with \(a>b\) such that \[ 7!|(x^a-x^b) \] for all integers \( x.\)
Find the smallest possible value of \( a+b.\)
Clarification:
\(!\) denotes the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).
by
Patrick Corn