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2024 SSMO Team Round Problems/Problem 8

Revision as of 15:44, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Three integers <math>0\le a\le b\le c< 229</math> satisfy the congruence <math>n^3 \equiv 1 \pmod{229}.</math> Given that <math>71^2 - 3</math> and <math>107^2 +...")
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Problem

Three integers $0\le a\le b\le c< 229$ satisfy the congruence $n^3 \equiv 1 \pmod{229}.$ Given that $71^2 - 3$ and $107^2 + 1$ are both multiples of $229,$ find the value of $b.$

Solution

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