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Omni-MATH / For positive integers a and N, let r(a,N)∈{0,1,…,N−1} denote the remainder of a when divided by N. Determine the number of positive integers n≤1000000 for which r(n,1000)>r(n,1001)…

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problem

For positive integers aa and NN, let r(a,N)∈{0,1,…,N−1}r(a, N) \in\{0,1, \ldots, N-1\} denote the remainder of aa when divided by NN. Determine the number of positive integers n≤1000000n \leq 1000000 for which r(n,1000)>r(n,1001)r(n, 1000)>r(n, 1001).
Plain-text mathematical notation (without MathML)
For positive integers a and N, let r(a,N)∈{0,1,…,N−1} denote the remainder of a when divided by N. Determine the number of positive integers n≤1000000 for which r(n,1000)>r(n,1001).
Original LaTeX notation
For positive integers $a$ and $N$, let $r(a, N) \in\{0,1, \ldots, N-1\}$ denote the remainder of $a$ when divided by $N$. Determine the number of positive integers $n \leq 1000000$ for which $r(n, 1000)>r(n, 1001)$.

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task_id
dfad9a21-87b3-56c4-a981-fb47e71a86f5
task_key
test--dfad9a21-87b3-56c4-a981-fb47e71a86f5
task_revision_id
1
config / split
/ test

Official source

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