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Omni-MATH / For every natural number x, let P(x) be the product of the digits of the number x. Is there a natural number n such that the numbers P(n) and P(n²) are non-zero squares of natural …

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problem

For every natural number xx{}, let P(x)P(x) be the product of the digits of the number xx{}. Is there a natural number nn{} such that the numbers P(n)P(n) and P(n2)P(n^2) are non-zero squares of natural numbers, where the number of digits of the number nn{} is equal to (a) 2021 and (b) 2022?
Plain-text mathematical notation (without MathML)
For every natural number x, let P(x) be the product of the digits of the number x. Is there a natural number n such that the numbers P(n) and P(n²) are non-zero squares of natural numbers, where the number of digits of the number n is equal to (a) 2021 and (b) 2022?
Original LaTeX notation
For every natural number $x{}$, let $P(x)$ be the product of the digits of the number $x{}$. Is there a natural number $n{}$ such that the numbers $P(n)$ and $P(n^2)$ are non-zero squares of natural numbers, where the number of digits of the number $n{}$ is equal to (a) 2021 and (b) 2022?

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Source and history

task_id
7387ae05-2735-51eb-924b-d24b264cf3b9
task_key
test--7387ae05-2735-51eb-924b-d24b264cf3b9
task_revision_id
1
config / split
/ test

Official source

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