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Omni-MATH / A sequence of positive integers is defined by a₀=1 and a_(n+1)=a_(n)²+1 for each n≥0. Find gcd(a₉₉₉,a₂₀₀₄).

Problem

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problem

A sequence of positive integers is defined by a0=1a_{0}=1 and an+1=an2+1a_{n+1}=a_{n}^{2}+1 for each n≥0n \geq 0. Find gcd(a999,a2004)\operatorname{gcd}(a_{999}, a_{2004}).
Plain-text mathematical notation (without MathML)
A sequence of positive integers is defined by a₀=1 and a_(n+1)=a_(n)²+1 for each n≥0. Find gcd(a₉₉₉,a₂₀₀₄).
Original LaTeX notation
A sequence of positive integers is defined by $a_{0}=1$ and $a_{n+1}=a_{n}^{2}+1$ for each $n \geq 0$. Find $\operatorname{gcd}(a_{999}, a_{2004})$.

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Source and history

task_id
0e660ff2-d23d-5c8d-8434-dfc285fcb7d7
task_key
test--0e660ff2-d23d-5c8d-8434-dfc285fcb7d7
task_revision_id
1
config / split
/ test

Official source

initial import