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Omni-MATH / Let us say that a pair of distinct positive integers is nice if their arithmetic…

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problem

Let us say that a pair of distinct positive integers is nice if their arithmetic mean and their geometric mean are both integer. Is it true that for each nice pair there is another nice pair with the same arithmetic mean? (The pairs (a,b)(a, b) and (b,a)(b, a) are considered to be the same pair.)
Plain-text mathematical notation (without MathML)
Let us say that a pair of distinct positive integers is nice if their arithmetic mean and their geometric mean are both integer. Is it true that for each nice pair there is another nice pair with the same arithmetic mean? (The pairs (a,b) and (b,a) are considered to be the same pair.)
Original LaTeX notation
Let us say that a pair of distinct positive integers is nice if their arithmetic mean and their geometric mean are both integer. Is it true that for each nice pair there is another nice pair with the same arithmetic mean? (The pairs $(a, b)$ and $(b, a)$ are considered to be the same pair.)

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Source and history

task_id
ca668461-0315-5eb7-bcb3-d9865f8d45ca
task_key
test--ca668461-0315-5eb7-bcb3-d9865f8d45ca
task_revision_id
1
config / split
/ test

Official source

initial import