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MathNet 2019-part-06 — 184 problems (EN–VI) Question 32

Math Olympiad Vault · MathNet 2019-part-06 — 184 problems (EN–VI)

Question 32

It is given a graph whose vertices are positive integers and an edge between numbers $a$ and $b$ exists if and only if
$$
a+b+1 \mid a^{2}+b^{2}+1 .
$$
Is this graph connected?