Number Theory problems
This area contains 190 revision-pinned source placements and 4 reviewed canonical dossiers. Placements may include aliases or duplicate claims.
Reviewed dossiers
Source placement records
- Büchi's problem on sufficiently large sequences of square numbers with constant second difference.
- Carmichael's totient function conjecture
- Catalan–Dickson conjecture on aliquot sequences
- Exponent pair conjecture
- The Gauss circle problem
- Grimm's conjecture
- Hall's conjecture
- Lehmer's totient problem
- Magic square of squares
- Mahler's 3/2 problem
- Newman's conjecture
- Scholz conjecture
- Singmaster's conjecture
- perfect numbers
- almost perfect numbers
- idoneal numbers
- amicable numbers
- betrothed numbers
- relatively prime
- Giuga numbers
- Lychrel numbers
- Taxicab(5, 2, n)
- covering system
- normal number
- irrational
- Erdős conjecture on arithmetic progressions
- Erdős–Turán conjecture on additive bases
- Gilbreath's conjecture on consecutive applications of the unsigned forward difference operator to the sequence of prime numbers.
- Goldbach's conjecture
- Lander, Parkin, and Selfridge conjecture
- Lemoine's conjecture
- Minimum overlap problem
- Recamán's sequence
- Skolem problem
- The values of g(k) and G(k) in Waring's problem
- Ulam numbers
- Determine growth rate of rk(N) (see Szemerédi's theorem)
- Class number problem
- Fontaine–Mazur conjecture
- Gan–Gross–Prasad conjecture
- Hermite's problem
- Hilbert's 9th problem
- Hilbert's 11th problem
- Hilbert's 12th problem
- Kummer–Vandiver conjecture
- supersingular primes
- Leopoldt's conjecture
- Stark conjectures (including Brumer–Stark conjecture)
- Characterize all algebraic number fields that have some power basis.
- Beilinson's conjectures about special values of L-functions.
- Find the value of the De Bruijn–Newman constant.
- Selberg class
- Hardy–Littlewood zeta function conjectures
- Keating–Snaith conjecture concerning the asymptotics of an integral involving the Riemann zeta function
- Hilbert–Pólya conjecture
- Lindelöf hypothesis
- The density hypothesis for zeroes of the Riemann zeta function.
- Location of nontrivial zeros of L-functions, especially conjectures concerning their critical lines:
- Grand Riemann hypothesis
- Generalized Riemann hypothesis for Selberg class
- Extended Riemann Hypothesis
- Generalized Riemann hypothesis
- Riemann hypothesis
- Montgomery's pair correlation conjecture
- Piltz divisor problem
- Dirichlet's divisor problem
- Ramanujan–Petersson conjecture
- Selberg's 1/4 conjecture
- Selberg's orthogonality conjecture
- Bombieri–Lang conjecture
- Erdős–Ulam problem
- Manin conjecture
- Sato–Tate conjecture
- Rational dense problem
- Vojta's conjecture
- n conjecture
- abc conjecture
- Szpiro's conjecture
- Zilber–Pink conjecture
- integer factorization
- discrete logarithm
- rational number
- Littlewood conjecture
- Schanuel's conjecture on the transcendence degree of certain field extensions of the rational numbers. In particular
- The four exponentials conjecture
- Euler's constant
- (exponential) periods
- non-quadratic
- simple continued fraction
- Beal's conjecture
- Brocard's problem
- Congruent number problem (a corollary to Birch and Swinnerton-Dyer conjecture, per Tunnell's theorem)
- Erdős–Moser problem
- Erdős–Straus conjecture
- Fermat–Catalan conjecture
- Goormaghtigh conjecture
- uniqueness conjecture for Markov numbers
- Pillai's conjecture
- sum of three perfect cubes
- Can every integer be written as a sum of four perfect cubes?
- Agoh–Giuga conjecture
- Agrawal's conjecture
- Artin's conjecture on primitive roots
- Brocard's conjecture
- Bunyakovsky conjecture
- Catalan's Mersenne conjecture
- Dickson's conjecture
- Dubner's conjecture
- Elliott–Halberstam conjecture on the distribution of prime numbers in arithmetic progressions.
- Erdős–Mollin–Walsh conjecture
- Feit–Thompson conjecture
- Fortune's conjecture that no Fortunate number is composite.
- The Gaussian moat problem
- Gillies' conjecture on the distribution of prime divisors of Mersenne numbers.
- Goldbach conjecture
- Legendre's conjecture
- Twin prime conjecture
- Are there infinitely many primes of the form n 2 + 1 {\displaystyle n^{2}+1} {\displaystyle n^{2}+1}?
- New Mersenne conjecture
- Polignac's conjecture
- Schinzel's hypothesis H
- Selfridge's conjecture
- converse of Wolstenholme's theorem
- Mersenne numbers
- Are there any composite c satisfying 2 ≡ 1 (mod c)?
- Wieferich primes
- balanced primes
- cluster primes
- cousin primes
- Cullen primes
- Euclid primes
- Fibonacci primes
- Kummer primes
- Mersenne primes
- Newman–Shanks–Williams primes
- palindromic primes
- Pierpont primes
- prime quadruplets
- prime triplets
- Siegel's conjecture
- safe and Sophie Germain primes
- Wagstaff primes
- Wilson primes
- Wolstenholme primes
- Woodall primes
- Can a prime p satisfy 2 p − 1 ≡ 1 ( mod p 2 ) {\displaystyle 2^{p-1}\equiv 1{\pmod {p^{2}}}} {\displaystyle 2^{p-1}\equiv 1{\pmod
- Euclid–Mullin sequence
- Lucas–Wieferich primes
- For any given integer a > 0, are there infinitely many primes p such that a ≡ 1 (mod p)?
- repunit
- For any given integers k ≥ 1 , b ≥ 2 , c ≠ 0 {\displaystyle k\geq 1,b\geq 2,c\neq 0} {\displaystyle k\geq 1,b\geq 2,c\neq 0}, with
- Fermat number
- André–Oort conjecture (Jonathan Pila, Ananth Shankar, Jacob Tsimerman, 2021)
- Duffin–Schaeffer theorem (Dimitris Koukoulopoulos, James Maynard, 2019)
- Main conjecture in Vinogradov's mean-value theorem (Jean Bourgain, Ciprian Demeter, Larry Guth, 2015)
- Goldbach's weak conjecture (Harald Helfgott, 2013)
- Existence of bounded gaps between arbitrarily large primes (Yitang Zhang, Polymath8, James Maynard, 2013)
- Sidon set problem (Javier Cilleruelo, Imre Z. Ruzsa, and Carlos Vinuesa, 2010)
- Serre's modularity conjecture (Chandrashekhar Khare and Jean-Pierre Wintenberger, 2008)
- Green–Tao theorem (Ben J. Green and Terence Tao, 2004)
- Catalan's conjecture (Preda Mihăilescu, 2002)
- Erdős–Graham problem (Ernest S. Croot III, 2000)
- Lafforgue's theorem (Laurent Lafforgue, 1998)
- Fermat's Last Theorem (Andrew Wiles and Richard Taylor, 1995)