Divisibility Of Power Differences

Let a a and b b be positive integers with a>ba>b such that 7!(xaxb) 7!\Big|\big(x^a-x^b\big) for all integers x. x.

Find the smallest possible value of a+b. a+b.

Clarification: !! denotes the factorial notation. For example, 8!=1×2×3××88! = 1\times2\times3\times\cdots\times8 .

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