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Omni-MATH / Let a₁=3, and for n≥1, let a_(n+1)=(n+1)a_(n)−n. Find the smallest m≥2005 such that a_(m+1)−1∣a_(m)²−1.

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problem

Let a1=3a_{1}=3, and for n≥1n \geq 1, let an+1=(n+1)an−na_{n+1}=(n+1) a_{n}-n. Find the smallest m≥2005m \geq 2005 such that am+1−1∣am2−1a_{m+1}-1 \mid a_{m}^{2}-1.
Plain-text mathematical notation (without MathML)
Let a₁=3, and for n≥1, let a_(n+1)=(n+1)a_(n)−n. Find the smallest m≥2005 such that a_(m+1)−1∣a_(m)²−1.
Original LaTeX notation
Let $a_{1}=3$, and for $n \geq 1$, let $a_{n+1}=(n+1) a_{n}-n$. Find the smallest $m \geq 2005$ such that $a_{m+1}-1 \mid a_{m}^{2}-1$.

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Source and history

task_id
66ac6562-d1e9-5969-b6e2-6245be009bc1
task_key
test--66ac6562-d1e9-5969-b6e2-6245be009bc1
task_revision_id
1
config / split
/ test

Official source

initial import