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Indian Mathematical Olympiad 1987 - Problem 3

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August 13, 2009
modular arithmeticalgebra proposedalgebra

Problem Statement

Let T T be the set of all triplets (a,b,c) (a,b,c) of integers such that 1≤a<b<c≤6 1 \leq a < b < c \leq 6 For each triplet (a,b,c) (a,b,c) in T T, take number a⋅b⋅c a\cdot b \cdot c. Add all these numbers corresponding to all the triplets in T T. Prove that the answer is divisible by 7.
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