Concept
Primality test
A computation certifying that a number is composite without producing a factor. Raising a base to one less than the number is the cheapest such test, and the composites it cannot catch are exactly those whose unit orders all divide one less than the number.
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Necklaces that prove a theorem
Thread five beads in two colours, thirty-two ways. Two of them are all one colour; the other thirty fall into rings of five. That count, and nothing else, is Fermat's little theorem.
The exponent that is smaller than Euler's
Euler's theorem raises every unit to the count of the units and gets one. The smallest exponent that works for all of them at once is often much smaller — and a composite is invisible to Fermat's test exactly when that smaller number divides n − 1.
Named alongside it
The objects these essays reach for when they reach for this one.
CompositeCounting two waysModular arithmeticOrderPrimesCyclic groupDivisorExhaustive searchFermats little theoremGroup actionModulusOrbit