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Let a a a and b b b be positive integers with a>ba>ba>b such that 7!∣(xa−xb) 7!\Big|\big(x^a-x^b\big) 7!∣∣∣(xa−xb) for all integers x. x.x.
Find the smallest possible value of a+b. a+b.a+b.
Clarification: !!! denotes the factorial notation. For example, 8!=1×2×3×⋯×88! = 1\times2\times3\times\cdots\times8 8!=1×2×3×⋯×8.
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