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2023 WSMO Team Round Problems/Problem 8

Revision as of 15:37, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>f(x)=\sqrt{x-\sqrt{x-\sqrt{x-\ldots}}}.</math> Find the modulo 1000 on the minimum integer <math>a</math> such <math>f(f(f(f(f(a)))))</math> is a positi...")
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Problem

Let $f(x)=\sqrt{x-\sqrt{x-\sqrt{x-\ldots}}}.$ Find the modulo 1000 on the minimum integer $a$ such $f(f(f(f(f(a)))))$ is a positive integer.

Solution

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