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Omni-MATH / A four-digit positive integer is called [i]virtual[/i] if it has the form…

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problem

A four-digit positive integer is called [i]virtual[/i] if it has the form abab¯\overline{abab}, where aa and bb are digits and a≠0a \neq 0. For example 2020, 2121 and 2222 are virtual numbers, while 2002 and 0202 are not. Find all virtual numbers of the form n2+1n^2+1, for some positive integer nn.
Plain-text mathematical notation (without MathML)
A four-digit positive integer is called [i]virtual[/i] if it has the form (abab)¯, where a and b are digits and a≠0. For example 2020, 2121 and 2222 are virtual numbers, while 2002 and 0202 are not. Find all virtual numbers of the form n²+1, for some positive integer n.
Original LaTeX notation
A four-digit positive integer is called [i]virtual[/i] if it has the form $\overline{abab}$, where $a$ and $b$ are digits and $a \neq 0$. For example 2020, 2121 and 2222 are virtual numbers, while 2002 and 0202 are not. Find all virtual numbers of the form $n^2+1$, for some positive integer $n$.

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Source and history

task_id
73f5b2cb-6d43-5766-abba-cefeec7669f1
task_key
test--73f5b2cb-6d43-5766-abba-cefeec7669f1
task_revision_id
1
config / split
/ test

Official source

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