In mathematics, Carmichael's totient function conjecture concerns the multiplicity of values of Euler's totient function φ(n), which counts the number...

with multiplicity k = 1. Carmichael's totient function conjecture is the statement that there is no such m. A perfect totient number is an integer that...

although they are not primes), Carmichael's totient function conjecture, Carmichael's theorem, and the Carmichael function, all significant in number theory...

with constant second difference. Carmichael's totient function conjecture: do all values of Euler's totient function have multiplicity greater than 1...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

ideal system of coins. In number theory, all powers of three are perfect totient numbers. The sums of distinct powers of three form a Stanley sequence,...

totient function. In 1998, he published a paper that studied in detail the range of this function and established that Carmichael's totient function conjecture...

nontotient is a positive integer n which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(x) = n has no solution...

number 1: for instance, the formulas for Euler's totient function or for the sum of divisors function are different for prime numbers than they are for 1...

Unsolved problem in mathematics Can the totient function of a composite number n {\displaystyle n} divide n − 1 {\displaystyle n-1} ? More unsolved problems...

Mertens function zero 2137 – prime of the form 2p-1 2138 – Mertens function zero 2141 – Sophie Germain prime 2142 – sum of the totient function for the...

produces an infinite quantity of Carmichael numbers is an open question (though it is implied by Dickson's conjecture). Paul Erdős heuristically argued...

However, the following is true: If c ≡ d (mod φ(m)), where φ is Euler's totient function, then ac ≡ ad (mod m)—provided that a is coprime with m. For cancellation...

proof of the Goldbach conjecture". In the movie, this number is known as a "Martian prime". Cunningham chain Double exponential function Fermat number Perfect...

= pentagonal number, sum of totient function for first 61 integers 1163 = smallest prime > 342. See Legendre's conjecture. Chen prime. 1164 = number of...

cosine functions, all continuous, may converge pointwise to a discontinuous function such as a step function. Carmichael's totient function conjecture was...

integers below it. That is, m − φ(m) = n, where φ stands for Euler's totient function, has no solution for m. The cototient of n is defined as n − φ(n),...

a prime factor that is not a factor of any smaller Fibonacci number (Carmichael's theorem). As a result, 8 and 144 (F6 and F12) are the only Fibonacci...

theorem Proofs of Fermat's little theorem Fermat quotient Euler's totient function Noncototient Nontotient Euler's theorem Wilson's theorem Primitive...

according to the prime number theorem; also, a version of Goldbach's conjecture has been extended to them. There are infinitely many lucky numbers. Twin...

(m)>\varphi (n)} where φ {\displaystyle \varphi } is Euler's totient function. The first few sparsely totient numbers are: 2, 6, 12, 18, 30, 42, 60, 66, 90, 120...

problem in mathematics Are any Fortunate numbers composite? (Fortune's conjecture) More unsolved problems in mathematics In number theory, a Fortunate number...

(Perfect totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A002997 (Carmichael numbers)"...

of four distinct triangular numbers in geometric progression. It was conjectured by Polish mathematician Kazimierz Szymiczek to be impossible and was...

Assuming the conjecture holds, this sequence of primes begins 2, 3, 2, 5, 2, 3, 7, 2 (sequence A073751 in the OEIS). Alaoglu and Erdős's conjecture would also...

Sierpiński number. In private correspondence with Paul Erdős, Selfridge conjectured that 78,557 was the smallest Sierpiński number. No smaller Sierpiński...

sequence is the set of primes p such that b is a primitive root modulo p. A conjecture of Emil Artin is that this sequence contains 37.395..% of the primes (for...

2{\pmod {3}}\quad {\text{then}}\quad x^{3}\equiv 8{\pmod {9}}.} It is conjectured that every integer (positive or negative) not congruent to ±4 modulo...

prime numbers. Indeed, theorems analogous to Goldbach's conjecture and the twin prime conjecture are known for practical numbers: every positive even integer...

has not been generalized in this way: by the (now proven) Stanley–Wilf conjecture, the number of such permutations is singly exponential, and the Bell numbers...