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Omni-MATH / Consider two positive integers a and b such that a^(n+1)+b^(n+1) is divisible by a^(n)+b^(n) for infi nitely many positive integers n. Is it necessarily true that a=b? (Boris Frenk…

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problem

Consider two positive integers aa and bb such that an+1+bn+1a^{n+1} + b^{n+1} is divisible by an+bna^n + b^n for infi nitely many positive integers nn. Is it necessarily true that a=ba = b? (Boris Frenkin)
Plain-text mathematical notation (without MathML)
Consider two positive integers a and b such that a^(n+1)+b^(n+1) is divisible by a^(n)+b^(n) for infinitely many positive integers n. Is it necessarily true that a=b?

(Boris Frenkin)
Original LaTeX notation
Consider two positive integers $a$ and $b$ such that $a^{n+1} + b^{n+1}$ is divisible by $a^n + b^n$ for infinitely many positive integers $n$. Is it necessarily true that $a = b$?

(Boris Frenkin)

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Source and history

task_id
a6d414c2-bfa5-5959-8a2b-fc36232f692b
task_key
test--a6d414c2-bfa5-5959-8a2b-fc36232f692b
task_revision_id
1
config / split
/ test

Official source

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