1

Part of 2012 Austria Beginners' Competition

Problems(1)

14 divides ab if 7a + 8b = 14c + 28d

Source: Austria Beginners' Competition 2012 p1

a, b, c

d

be four integers such that

7a + 8b = 14c + 28d

. Prove that the product

a\cdot b

is always divisible by

14

number theorydividesdivisible