Fermat's Little, Tiny, and Huge Theorems
Fermat's Little, Tiny, and Huge Theorems: a riff on Fermat.
Content note: Mild language.
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Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.
Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2025-08-07-fermat-s-other-theorems--fermat-s-little-tiny-and-huge-theorems/ (CC BY-NC 4.0)Transcript
FERMAT'S LITTLE THEOREM: If p is prime, then aᵖ − a is a multiple of p. EX: 10¹³ − 10 is a multiple of 13. / FERMAT'S TINY THEOREM (same, in tiny print). EX: 2³ − 2 is a multiple of 3. / FERMAT'S HUGE THEOREM: Get this: if p is prime, then aᵖ − a is, no joke, a friggin' *exact multiple* of p. EX: 1000⁷⁹¹⁹ − 1000 is a multiple of 7919.