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12 divides (b - a)(c - a)(d - a)(d - c)(d - b)( c - b)

Source: Eotvos 1925 p1

September 10, 2024
number theorydividesdivisible

Problem Statement

Let a,b,c,da,b, c,d be four integers. Prove that the product of the six differences b−a,c−a,d−a,d−c,d−b,c−bb - a,c - a,d - a,d - c,d - b, c - b is divisible by 1212.
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