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Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » Subtopicsort iconPosted by
Fixed-point logic with countingBlass✭✭0Logic » Finite Model Theorydberwanger
Order-invariant queriesSegoufin✭✭0Logic » Finite Model Theorydberwanger
Monadic second-order logic with cardinality predicatesCourcelle✭✭0Logic » Finite Model Theorydberwanger
Blatter-Specker Theorem for ternary relationsMakowsky✭✭0Logic » Finite Model Theorydberwanger
MSO alternation hierarchy over picturesGrandjean✭✭0Logic » Finite Model Theorydberwanger
Finite entailment of Positive Horn logicMartin✭✭0Logic » Finite Model TheoryLucSegoufin
Vertex Cover Integrality GapAtserias✭✭0Logic » Finite Model Theorydberwanger
Lonely runner conjectureCusick; Wills✭✭✭0Number Theorymdevos
MacEachen ConjectureMcEachen✭1Number Theorybillymac00
Chowla's cosine problemChowla✭✭✭0Number Theorymdevos
Quartic rationally derived polynomialsBuchholz; MacDougall✭✭✭0Number Theorymdevos
A discrete iteration related to Pierce expansionsShallit✭✭1Number Theoryshallit
Algebraic independence of pi and e✭✭✭0Number Theoryporton
Odd perfect numbersAncient/folklore✭✭✭1Number Theoryazi
Diophantine quintuple conjecture✭✭1Number Theorymaxal
Twin prime conjecture✭✭✭✭0Number Theorykaushiks.nitt
Polignac's Conjecturede Polignac✭✭✭0Number TheoryHugh Barker
Special PrimesGeorge BALAN✭1Number Theorymaththebalans
Primitive pythagorean n-tuple tree✭✭0Number Theorytsihonglau
3 is a primitive root modulo primes of the form 16 q^4 + 1, where q>3 is prime✭✭0Number Theoryprinceps
Erdős–Straus conjectureErdos; Straus✭✭1Number TheoryACW
Lucas Numbers Modulo m✭✭1Number TheoryMartin Erickson
Sum of prime and semiprime conjectureGeoffrey Marnell✭✭0Number Theoryprinceps
Giuga's Conjecture on PrimalityGiuseppe Giuga✭✭0Number Theoryprinceps
Alexa's Conjecture on PrimalityAlexa✭✭0Number Theoryprinceps
Birch & Swinnerton-Dyer conjecture✭✭✭✭0Number Theoryeyoong
The Erdos-Turan conjecture on additive basesErdos; Turan✭✭✭✭0Number Theory » Additive N.T.mdevos
Goldbach conjectureGoldbach✭✭✭✭0Number Theory » Additive N.T.Benschop
Are there an infinite number of lucky primes?Lazarus: Gardiner: Metropolis; Ulam✭1Number Theory » Additive N.T.cubola zaruka
The Riemann HypothesisRiemann✭✭✭✭0Number Theory » Analytic N.T.eric
Schanuel's ConjectureSchanuel✭✭✭✭0Number Theory » Analytic N.T.Charles
Distribution and upper bound of mimic numbersBhattacharyya✭✭1Number Theory » Analytic N.T.facility_cttb@i...
Lindelöf hypothesisLindelöf✭✭0Number Theory » Analytic N.T.porton
Euler-Mascheroni constant✭✭✭0Number Theory » Analytic N.T.Juggernaut
Is Skewes' number e^e^e^79 an integer?✭✭0Number Theory » Analytic N.T.VladimirReshetnikov
Are all Fermat Numbers square-free?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are there only finite Fermat Primes?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are all Mersenne Numbers with prime exponent square-free?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are there infinite number of Mersenne Primes?✭✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Olson's ConjectureOlson✭✭0Number Theory » Combinatorial N.T.mdevos
Few subsequence sums in Z_n x Z_nBollobas; Leader✭✭0Number Theory » Combinatorial N.T.mdevos
Gao's theorem for nonabelian groupsDeVos✭✭0Number Theory » Combinatorial N.T.mdevos
Sets with distinct subset sumsErdos✭✭✭0Number Theory » Combinatorial N.T.mdevos
The 3n+1 conjectureCollatz✭✭✭0Number Theory » Combinatorial N.T.dododododo
Odd incongruent covering systemsErdos; Selfridge✭✭✭0Number Theory » Combinatorial N.T.Robert Samal
Covering systems with big moduliErdos; Selfridge✭✭0Number Theory » Combinatorial N.T.Robert Samal
Divisibility of central binomial coefficientsGraham✭✭1Number Theory » Combinatorial N.T.maxal
Davenport's constant✭✭✭0Number Theory » Combinatorial N.T.mdevos
Snevily's conjectureSnevily✭✭✭1Number Theory » Combinatorial N.T.mdevos
Frobenius number of four or more integers✭✭1Number Theory » Combinatorial N.T.maxal

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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