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Counter-Example to Fermat's Conjecture
publish date: 2026/05/23 05:12:48.806014 UTC
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Pierre de Fermat conjectured that \(2^{2^n} + 1\) is prime for every natural number \(n\). Which mathematician disproved this conjecture, and for which value of \(n\)?
Correct Answer
Euler; \(n = 5\)
Explanation
Leonhard Euler (1707–1783) showed that \(2^{2^5} + 1 = 4{,}294{,}967{,}297\) is not prime, since it is divisible by 641. This is a classic example of how a well-supported conjecture can still be false — one counter-example is sufficient to disprove it.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012