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Numbers

Euler's totient

How many numbers below n share no factors with n? φ(n) counts them.

Euler's totient φ(n) counts how many positive integers below n are coprime to n.

Try it

φ(10)

Coprime to 10 below it: 1, 3, 7, 9. So φ(10) = 4.

Used in RSA encryption — and famously, e^(iπ) + 1 = 0 lives in Euler's universe.