Linked from

The 21 pages that link to Euler's totient function, each with the reason it gives.

• Leonhard EulerBroader topic: Euler studied this counting function and established a theorem that links it to modular arithmetic.

• Coprime integersRelated: It counts the residues that can have multiplicative inverses modulo n.

• Cyclotomic fieldRelated: The degree of the nth cyclotomic field is φ(n).

• Cyclotomic polynomialRelated: The degree of Φₙ(x) is φ(n), the number of primitive nth roots.

• RSA cryptosystemRelated: Its value for RSA’s modulus helps determine the private exponent.

• Multiplicative functionBroader topic: Coprime residue classes combine to give φ(ab)=φ(a)φ(b) when a and b are coprime.

• Divisor functionCompared with: It counts integers defined by coprimality, rather than divisors of n.

• Möbius functionRelated: A divisor sum involving the Möbius function gives an exact formula for it.

• Dirichlet characterRelated: It gives the order of the unit group modulo n and thus the number of character values to organize.

• Prime number theorem for arithmetic progressionsRelated: It determines the predicted share of primes in each reduced residue class.

• Euler's criterionRelated: For prime p, the exponent in Euler's criterion is half of φ(p).

• Shor's algorithmRelated: Factoring reductions use totient-related order information to obtain nontrivial factors.

• Bombieri–Vinogradov theoremRelated: It gives the expected share of primes in each admissible residue class.

• Finite cyclic groupRelated: A cyclic group of order n has exactly φ(n) generators.

• Arithmetic functionBroader topic: It measures how many residue classes modulo n are invertible.

• Solovay–Strassen primality testRelated: Its multiplicative-group interpretation helps explain exponentiation modulo primes and composites.

• Siegel–Walfisz theoremRelated: The expected prime count in each eligible class is normalized by φ(q).

• Brun–Titchmarsh theoremRelated: It normalizes the bound by the number of eligible residue classes.

• Zsigmondy's theoremRelated: Orders modulo a prime divide its totient, constraining primes that could divide a cyclotomic value.

• Aliquot sumCompared with: It counts integers by coprimality instead of summing proper divisors.

• Unit (ring theory)Related: Its value counts the units in the ring of integers modulo n.