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Number Theory


TitleAuthor(s)Imp.¹Rec.²Topic » Subtopicsort iconPosted by
Lonely runner conjectureCusick; Wills✭✭✭0mdevos
MacEachen ConjectureMcEachen✭1billymac00
Chowla's cosine problemChowla✭✭✭0mdevos
Quartic rationally derived polynomialsBuchholz; MacDougall✭✭✭0mdevos
A discrete iteration related to Pierce expansionsShallit✭✭1shallit
Algebraic independence of pi and e✭✭✭0porton
Odd perfect numbersAncient/folklore✭✭✭1azi
Diophantine quintuple conjecture✭✭1maxal
Twin prime conjecture✭✭✭✭0kaushiks.nitt
Polignac's Conjecturede Polignac✭✭✭0Hugh Barker
Special PrimesGeorge BALAN✭1maththebalans
Primitive pythagorean n-tuple tree✭✭0tsihonglau
3 is a primitive root modulo primes of the form 16 q^4 + 1, where q>3 is prime✭✭0princeps
Erdős–Straus conjectureErdos; Straus✭✭1ACW
Lucas Numbers Modulo m✭✭1Martin Erickson
Sum of prime and semiprime conjectureGeoffrey Marnell✭✭0princeps
Giuga's Conjecture on PrimalityGiuseppe Giuga✭✭0princeps
Alexa's Conjecture on PrimalityAlexa✭✭0princeps
Birch & Swinnerton-Dyer conjecture✭✭✭✭0eyoong
The Erdos-Turan conjecture on additive basesErdos; Turan✭✭✭✭0Additive N.T.mdevos
Goldbach conjectureGoldbach✭✭✭✭0Additive N.T.Benschop
Are there an infinite number of lucky primes?Lazarus: Gardiner: Metropolis; Ulam✭1Additive N.T.cubola zaruka
The Riemann HypothesisRiemann✭✭✭✭0Analytic N.T.eric
Schanuel's ConjectureSchanuel✭✭✭✭0Analytic N.T.Charles
Distribution and upper bound of mimic numbersBhattacharyya✭✭1Analytic N.T.facility_cttb@i...
Lindelöf hypothesisLindelöf✭✭0Analytic N.T.porton
Euler-Mascheroni constant✭✭✭0Analytic N.T.Juggernaut
Is Skewes' number e^e^e^79 an integer?✭✭0Analytic N.T.VladimirReshetnikov
Are all Fermat Numbers square-free?✭✭✭0Analytic N.T.kurtulmehtap
Are there only finite Fermat Primes?✭✭✭0Analytic N.T.kurtulmehtap
Are all Mersenne Numbers with prime exponent square-free?✭✭✭0Analytic N.T.kurtulmehtap
Are there infinite number of Mersenne Primes?✭✭✭✭0Analytic N.T.kurtulmehtap
Olson's ConjectureOlson✭✭0Combinatorial N.T.mdevos
Few subsequence sums in Z_n x Z_nBollobas; Leader✭✭0Combinatorial N.T.mdevos
Gao's theorem for nonabelian groupsDeVos✭✭0Combinatorial N.T.mdevos
Sets with distinct subset sumsErdos✭✭✭0Combinatorial N.T.mdevos
The 3n+1 conjectureCollatz✭✭✭0Combinatorial N.T.dododododo
Odd incongruent covering systemsErdos; Selfridge✭✭✭0Combinatorial N.T.Robert Samal
Covering systems with big moduliErdos; Selfridge✭✭0Combinatorial N.T.Robert Samal
Divisibility of central binomial coefficientsGraham✭✭1Combinatorial N.T.maxal
Davenport's constant✭✭✭0Combinatorial N.T.mdevos
Snevily's conjectureSnevily✭✭✭1Combinatorial N.T.mdevos
Frobenius number of four or more integers✭✭1Combinatorial N.T.maxal
Singmaster's conjectureSingmaster✭✭1Combinatorial N.T.Zach Teitler
A sextic counterexample to Euler's sum of powers conjectureEuler✭✭1Computational N.T.maxal
Counterexamples to the Baillie-PSW primality test✭✭1Computational N.T.maxal
Wall-Sun-Sun primes and Fibonacci divisibility✭✭0Computational N.T.adudzik
Magic square of squaresLaBar✭✭1Computational N.T.maxal
Perfect cuboid✭✭0Computational N.T.tsihonglau

Imp.¹: Importance (Low ✭, Medium ✭✭, High ✭✭✭, Outstanding ✭✭✭✭)
Rec.²: Recommended for undergraduates.

Note: Resolved problems from this section may be found in Solved problems.

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