1

Part of 1980 Czech And Slovak Olympiad IIIA

Problems(1)

1980^{197} | (k + 1)(k + 2)...(k + 1980)

Source: Czech and Slovak Olympiad 1980, National Round, Problem 1

Prove that for every nonnegative integer

k

there is a product

(k + 1)(k + 2)...(k + 1980)

1980^{197}

number theorydividesdivisible