Lehmer's conjecture, also known as the Lehmer's Mahler measure problem, is a problem in number theory raised by Derrick Henry Lehmer. The conjecture asserts...

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

also formulated Lehmer's conjecture and participated in the Cunningham project. Lehmer died in Berkeley on May 22, 1991. Lucas–Lehmer–Riesel test Størmer's...

subspace to itself? Kung–Traub conjecture on the optimal order of a multipoint iteration without memory Lehmer's conjecture on the Mahler measure of non-cyclotomic...

{\displaystyle p(z)=z,} or p {\displaystyle p} is a cyclotomic polynomial. (Lehmer's conjecture) There is a constant μ > 1 {\displaystyle \mu >1} such that if p...

or a set of amicable or sociable numbers? (Catalan's aliquot sequence conjecture) More unsolved problems in mathematics In mathematics, an aliquot sequence...

artist Derrick Lehmer (disambiguation) Lehmer–Schur algorithm, in mathematics, named after Derrick Henry Lehmer Lehmer code Lehmer's conjecture (also known...

{\displaystyle n-1} ? More unsolved problems in mathematics In mathematics, Lehmer's totient problem asks whether there is any composite number n such that...

In mathematics, Montgomery's pair correlation conjecture is a conjecture made by Hugh Montgomery (1973) that the pair correlation between pairs of zeros...

OEIS). Lehmer (1947) conjectured that τ ( n ) ≠ 0 {\displaystyle \tau (n)\neq 0} for all n {\displaystyle n} , an assertion sometimes known as Lehmer's conjecture...

the tau conjecture may refer to one of Lehmer's conjecture on the non-vanishing of the Ramanujan tau function The Ramanujan–Petersson conjecture on the...

problems in mathematics In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even...

and the availability of new techniques such as the Lucas–Lehmer test, that Mersenne's conjecture contained five errors, namely two entries are composite...

p = 1 (mod 4) and p ≠ 5. The same author also proved Woltman's conjecture that the Lehmer symbols for starting values 4 and 10 when p is not 2 or 5 are...

Q {\displaystyle \mathbb {Q} } ). abc conjecture Birch and Swinnerton-Dyer conjecture Elliptic Lehmer conjecture Heath-Brown–Moroz constant Height of a...

Terence Tao. Montgomery's pair correlation conjecture Csordas, George; Smith, Wayne; Varga, Richard S. (1994), "Lehmer pairs of zeros, the de Bruijn-Newman...

function fields is unconditionally true. The best general result on Lehmer's conjecture is the weaker estimate h ^ ( P ) ≥ c ( E / K ) / [ K ( P ) : K ]...

polynomials implies M ( f ) ≥ 1 {\displaystyle M(f)\geq 1} . See also Lehmer's conjecture. The Mahler measure is multiplicative, i.e. if f = g h {\displaystyle...

known Salem number is the largest real root of Lehmer's polynomial (named after Derrick Henry Lehmer) P ( x ) = x 10 + x 9 − x 7 − x 6 − x 5 − x 4 −...

covering set {3, 5, 7, 13, 19, 37, 73}. Five years later, he and Sierpiński conjectured that 78,557 is the smallest Sierpinski number, and thus the answer to...

. {\displaystyle 2k.} Andrica's conjecture, Brocard's conjecture, Legendre's conjecture, and Oppermann's conjecture all suggest that the largest gaps...

consecutive P-smooth numbers, because all P-smooth numbers would be odd. Lehmer's method involves solving the Pell equation x 2 − 2 q y 2 = 1 {\displaystyle...

S2CID 123486171. Ram Murty, M.; Saradha, N. (2010). "Euler–Lehmer constants and a conjecture of Erdos". Journal of Number Theory. 130 (12): 2671–2681....

investigate conjectures and open problems in number theory, including the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, the ABC conjecture, the...

Mersenne primes is finite or infinite. The Lenstra–Pomerance–Wagstaff conjecture claims that there are infinitely many Mersenne primes and predicts their...

Agoh–Giuga conjecture Von Staudt–Clausen theorem Dirichlet series Euler product Prime number theorem Prime-counting function Meissel–Lehmer algorithm Offset...

a given number is prime or composite without relying on mathematical conjectures such as the generalized Riemann hypothesis. The proof is also notable...

Mertens conjecture was proven false in 1985 by Andrew Odlyzko and Herman te Riele. However, the Riemann hypothesis is equivalent to a weaker conjecture on...

University of California, Berkeley under Derrick Henry Lehmer for a thesis entitled "Proof of a Conjecture of Gauss on Class Number Two". After holding a position...

computers to search for a counterexample to some conjectures. The first conjecture (Agrawal's conjecture) was the basis for the formulation of the first...