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2017 Guts #20: n % 1000 > n % 1001

Source:

February 21, 2017

number theory

Problem Statement

For positive integers

a

and

N

, let

r(a, N) \in \{0, 1, \dots, N - 1\}

denote the remainder of

a

when divided by

N

. Determine the number of positive integers

n \le 1000000

for which

r(n, 1000) > r(n, 1001).

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