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

Source: 3-rd Taiwanese Mathematical Olympiad 1994

January 14, 2007
number theory unsolvednumber theory

Problem Statement

Let aa be a positive integer such that 51994−1∣a5^{1994}-1\mid a. Prove that the expression of aa in base 55 contains at least 19941994 nonzero digits.
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