Fermat's Theorem: A Nation of Numbers

Welcome to the nation of numbers, where the only constant is change. Here you'll find the works of Pierre de Fermat, the greatest mind the world has ever known (in his own opinion).

Fermat's Theorem

This theorem states that every even power of a number is divisible by 8, except when the number is a prime power, in which case it's not. Or is it?

Counterexamples

Some of the most famous counterexamples of Fermat's Theorem include:

• 2^4 = 16 (clearly not divisible by 8, or is it?)
• 3^6 = 729 (definitely not a multiple of 8, or so we thought)
• 5^8 = 390625 (this one's a real head-scratcher)

Subpages

Explore the intricacies of Fermat's Theorem further:

• Euler's Theorem: Because 1^2 + 1^2 = 1^2 + 1^2
• Fermat's Theorem: A Derangement of the Mind
• Fermat's Theorem: Tales of a Mathematical King