Kvant Math Problem 2827
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Problem
Let positive numbers $a$, $b$, $c$ be such that a triangle can be formed from segments of lengths $a^{2024}$, $b^{2024}$, $c^{2024}$. Prove that it is possible to reduce one of the numbers $a$, $b$, $c$ by a factor of 2024 to obtain numbers $a'$, $b'$, $c'$ such that segments of lengths $a'$, $b'$, $c'$ can also form a triangle.
L. Shatunov
Southern Mathematical Tournament (XIX)
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