MathDB

1

Part of 1925 Eotvos Mathematical Competition

Problems(1)

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

Source: Eotvos 1925 p1

9/10/2024
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.
number theorydividesdivisible