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Omni-MATH / Let P(n)=(n−1³)(n−2³)…(n−40³) for positive integers n. Suppose that d is the largest positive integer that divides P(n) for every integer n>2023. If d is a product of m (not necess…

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problem

Let P(n)=(n−13)(n−23)…(n−403)P(n)=\left(n-1^{3}\right)\left(n-2^{3}\right) \ldots\left(n-40^{3}\right) for positive integers nn. Suppose that dd is the largest positive integer that divides P(n)P(n) for every integer n>2023n>2023. If dd is a product of mm (not necessarily distinct) prime numbers, compute mm.
Plain-text mathematical notation (without MathML)
Let P(n)=(n−1³)(n−2³)…(n−40³) for positive integers n. Suppose that d is the largest positive integer that divides P(n) for every integer n>2023. If d is a product of m (not necessarily distinct) prime numbers, compute m.
Original LaTeX notation
Let $P(n)=\left(n-1^{3}\right)\left(n-2^{3}\right) \ldots\left(n-40^{3}\right)$ for positive integers $n$. Suppose that $d$ is the largest positive integer that divides $P(n)$ for every integer $n>2023$. If $d$ is a product of $m$ (not necessarily distinct) prime numbers, compute $m$.

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Source and history

task_id
e15127bf-8ab2-50f3-8df6-a5b41304c754
task_key
test--e15127bf-8ab2-50f3-8df6-a5b41304c754
task_revision_id
1
config / split
/ test

Official source

initial import