Question 3

For any natural number $$n$$, expressed in base $$10$$, let $$s(n)$$ denote the sum of all its digits. Find all natural numbers $$m$$ and $$n$$ such that $$m < n$$ and $$(s(n))^{2} = m$$ and $$(s(m))^{2} = n$$.

Correct Answer: e

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