IOM 2020, Блиц — Задача 15

The Blitz-contest of IOM-2020

Условие

For a positive integer $n$ and nonzero digits $a$, $b$, and $c$, let $A_n$ be the $n$-digit integer each of whose digits is equal to $a$; let $B_n$ be the $n$-digit integer each of whose digits is equal to $b$, and let $C_n$ be the $2n$-digit (not $n$-digit) integer each of whose digits is equal to $c$. Consider the triples $(a, b, c)$ for which there are at least two values of $n$ such that $C_n - B_n = A_n^2$. Find the maximal value of $a + b + c$ for such triples.

Отговори

Решение

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Оригинал в Архива: iom-2020-blitz-tasks.pdf · официални решения: iom-2020-blitz-answers.pdf