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If aaa, bbb, and ccc are positive integers that satisfy 30∣(a+b+c),30 {\large\mid} (a+b+c),30∣(a+b+c), is it also true that 30∣(a5+b5+c5)?30 {\large\mid} \big(a^5+b^5+c^5\big)?30∣(a5+b5+c5)?
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