3

Part of 1994 Taiwan National Olympiad

Problems(1)

$a$ in base $5$ contains at least $1994$ nonzero digits

Source: 3-rd Taiwanese Mathematical Olympiad 1994

a

be a positive integer such that

5^{1994}-1\mid a

. Prove that the expression of

a

5

contains at least

1994

nonzero digits.

number theory unsolvednumber theory