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Divisibilityhard
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For how many triples of positive integers (a,b,c)(a, b, c)(a,b,c) with 1≤a<b<c≤61 \le a < b < c \le 61≤a<b<c≤6 is the expression 2a+2b+2c2^a + 2^b + 2^c2a+2b+2c divisible by 7?