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Omni-MATH / Find all positive integers n≥1 such that there exists a pair (a,b) of positive integers, such that a²+b+3 is not divisible by the cube of any prime, and n=(ab+3b+8)/(a²+b+3).

Problem

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problem

Find all positive integers n≥1n\geq1 such that there exists a pair (a,b)(a,b) of positive integers, such that a2+b+3a^2+b+3 is not divisible by the cube of any prime, and n=ab+3b+8a2+b+3.n=\frac{ab+3b+8}{a^2+b+3}.
Plain-text mathematical notation (without MathML)
Find all positive integers n≥1 such that there exists a pair (a,b) of positive integers, such that a²+b+3 is not divisible by the cube of any prime, and n=(ab+3b+8)/(a²+b+3).
Original LaTeX notation
Find all positive integers $n\geq1$ such that there exists a pair $(a,b)$ of positive integers, such that $a^2+b+3$ is not divisible by the cube of any prime, and $$n=\frac{ab+3b+8}{a^2+b+3}.$$

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Source and history

task_id
b963c6f7-bc2e-5ab4-b733-4468f101b813
task_key
test--b963c6f7-bc2e-5ab4-b733-4468f101b813
task_revision_id
1
config / split
/ test

Official source

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