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Omni-MATH / For each positive integer n, define S(n) to be the smallest positive integer divisible by each of the positive integers 1,2,3,…,n. How many positive integers n with 1≤n≤100 have …

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problem

For each positive integer nn, define S(n)S(n) to be the smallest positive integer divisible by each of the positive integers 1,2,3,…,n1, 2, 3, \ldots, n. How many positive integers nn with 1≤n≤1001 \leq n \leq 100 have S(n)=S(n+4)S(n) = S(n+4)?
Plain-text mathematical notation (without MathML)
For each positive integer n, define S(n) to be the smallest positive integer divisible by each of the positive integers 1,2,3,…,n. How many positive integers n with 1≤n≤100 have S(n)=S(n+4)?
Original LaTeX notation
For each positive integer $n$, define $S(n)$ to be the smallest positive integer divisible by each of the positive integers $1, 2, 3, \ldots, n$. How many positive integers $n$ with $1 \leq n \leq 100$ have $S(n) = S(n+4)$?

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Source and history

task_id
b605c66e-c60b-5ca9-93b3-2e51724834c4
task_key
test--b605c66e-c60b-5ca9-93b3-2e51724834c4
task_revision_id
1
config / split
/ test

Official source

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