Partitions of \(n\) into \(x + y\)… to Lam--Litt conjecture
Partitions of \(n\) into \(x + y\)… to Number of primes \(p < n\) such…
- Partitions of \(n\) into \(x + y\) with \(x(x+1)/2 + y^2\) prime
- Square root of the absolute value of the determinant of the prime sum indicator matrix
- Determinant of odd composite sum indicator matrix
- Determinant of prime sum/difference matrix
- Determinant of square/cube sum matrix
- Numbers \(n\) such that \(n^2 + \pi(n)\) is prime
- Undirected circular permutations with adjacent products minus one all prime
- Ways to write \(n = x + y + z\) with six linear and quadratic forms prime
- Partitions \(n = p + q\) with \(p\), \(3p - 10\), and \((p - 1)q - 1\) prime
- Triples summing to \(n\) with \(2m+1\) and \(2m^3+1\) prime
- Smallest \(n\)-th power equal to a sum of consecutive immediately preceding positive \(n\)-th powers
- Sum of two numbers with prime conditions
- Ways to write \(n = x + y\) with \(2^x + y(y+1)/2\) prime
- Sequence designed to show there are infinitely many primes congruent to \(1\) modulo \(4\)
- Representations with prime conditions
- Ways to write \(n = x + y\) with \(nx + y\) and \(ny - x\) both prime
- Least \(m > 0\) such that \(\{2^k - k : k = 1, \dots, m\}\) covers all residues modulo \(n\)
- Representations \(n = k^2 + m\) (\(0 < k^2 \le m\)) with \(\sigma(k^2) + \phi(m)\) prime
- Number of ways to write \(n = p + q\) (\(q > 0\)) with \(p\) and \((\phi(p)\phi(q))^4 + 1\) prime
- Number of primes \(p < n\) such that \(p \phi(n - p) - 1\) is also prime
Values \(m = \sigma(k)\) ($0 < m… to Number of integers $0 < k \le…
- Values \(m = \sigma(k)\) (\(0 < m < 2n\)) with \(2n - 1 - m\) and \(2n - 1 + m\) prime
- Number of integers \(0 < k < n\) such that \(k \phi(n - k) + 1\) is a square
- Number of integers \(0 < k < n\) such that \((k + 1)^{\phi(n - k)} + k\) is prime
- Smallest \(x\) such that \(x \bmod \phi(x) = n\), or \(0\) if no such \(x\) exists
- Integers \(0 < k < n\) with \(p = k + \mathrm{prime}(n - k)\) and \(\mathrm{prime}(p) - p + 1\) prime
- Number of integers \(0 < k < n\) such that \(p = k + \phi(n - k)\) and \(2(n - p) + 1\) are both prime
- Number of \(0 < k < n-2\) with \(p = \phi(k) + \phi(n-k)/2 + 1\) and \(p_p - p \pm 1\) prime
- Prime quadruplets generated by \(p = 3\phi(k) + \phi(n-k) - 1\)
- Ordered ways to write \(2n = p + q\) with \(p, q\) and \(p_{p+2} + 2\) all prime
- Number of \(0 < k < n/2\) such that \(\phi(k)\phi(n-k)\) is a square
- Number of parts in the symmetric representation of \(\sigma(n)\)
- Ordered ways to write \(n = k + m\) with \(p_k + 4\) and \(p_{p_m} + 4\) both prime
- Ways to write \(n = k + m\) with \(p_k^2 - 2\), \(p_m^2 - 2\), and \(p_{p_m}^2 - 2\) all prime
- Number of \(0 < k < n\) such that \(\pi(kn)\) is prime
- Number of primes \(p \le (n+1)/2\) with \(\lfloor\sqrt{n-p}\rfloor\) prime
- Pairs \(\{j, k\}\) with \(0 < j < k \le n\), \(k \equiv 1 \pmod j\), and \(\pi(jn) \mid \pi(kn)\)
- Equal prime counts in adjacent intervals \((kn, (k+1)n)\) and \(((k+1)n, (k+2)n)\)
- Number of positive integers \(k < n\) such that \(n^2 - \pi(k n)\) is prime
- Number of primes \(p < n\) with \(\text{prime}(p)^2 + (\text{prime}(n) - 1)^2\) prime
- Number of integers \(0 < k \le n\) such that \(\pi(\pi(k n))\) is a square
Primitive roots of the form k²… to Asymptotics of an inner sum…
- Primitive roots of the form k² + 1
- Ways of writing \(n\) as an ordered sum of a triangular, square, and pentagonal number
- Largest smallest-base in a decomposition of \(n\) into at most four squares
- Least primitive prime divisor of the Franel numbers of order \(4\)
- Smallest \(k \ge 1\) such that the concatenation of \(k\) threes and \(\text{prime}(n)\) is prime
- Signed digit sums in bases \(b \ge 5\)
- Least index \(i\) for which \(\text{num}(\sigma_1(i)/i) - \text{den}(\sigma_1(i)/i) = n\)
- Sum of \(d \cdot \tau(d)\) over proper divisors \(d\) of \(n\)
- Difference between \(n \tau(n)\) and \(\sum_{d \mid n, d < n} d \tau(d)\)
- Least \(m\) such that \(m + n\) divides \(\mathrm{prime}(m) + \mathrm{prime}(n)\)
- Least \(m > 0\) coprime to \(n\) such that \(mn \mid C(m+n)\)
- Smallest prime factors of \(2^{2^n+2} + 3\)
- Smallest \(m \in \[1, n\]\) such that \(\binom{n}{m}\) is evil
- Odd part of the digital sum of \(3^n\) divided by the maximal power of \(3\)
- Floor of \(n^2\) divided by the sum of products of consecutive divisors of \(n\)
- Representations of \(n\) as the sum of two pentagonal and a generalized decagonal number
- Representations of \(n\) as a sum of generalized heptagonal, octagonal, and nonagonal numbers
- Partitions of \(n\) into distinct non-squarefree parts for \(n > 23\)
- Ways to write \(n\) as the sum of three elements of \(\{\lfloor T(x)/3 \rfloor : x \ge 1\}\)
- Asymptotics of an inner sum formula for \(a(n)\)
Catalan numbers modulo \(6\) to Sum of a triangular number, a…
- Catalan numbers modulo \(6\)
- A GCD-Driven Sequence with Universal Jumps
- Prime values in recurrence \(a(n+1) = |a(n) - \gcd(a(n), 7n+6)|\)
- Primes \(p\) such that \(n - (p n' - 1)\) and \(n + (p n' - 1)\) are both prime
- Sums of four binary palindromes
- Refining Lagrange's four-square theorem with \((5x^2 + 7y^2 + 9z^2)yz\) a square
- Additive decompositions of \(\pi(T(n))\)
- Additive decompositions of \(\pi(\frac{n(n+1)}{2} + 1)\)
- Representations of \(n\) as \(x^2 + \phi(y^2) + \phi(z^2)\)
- Sums of a cube, a square, and a positive triangular number
- Sums of a square and three weighted cubes
- Sums of a triangular number and three weighted cubes
- Recurrence for Rule 167 cellular automaton sequence
- Maximal run lengths in the second MSB of Tribonacci numbers \(T(n)\)
- Congruences \(a(n+k) \equiv a(n) \pmod k\) for hypergeometric values \({}_2F_1(n, -n; ; -1)\)
- The 1680-Conjecture
- The cup-of-coffee sequence
- Sum of four squares with square conditions
- Period of \(p\)-th powers modulo \(n\)
- Sum of a triangular number, a generalized pentagonal number, and a generalized heptagonal number
Symmetry of digit sum… to Realization of primes $p \equiv…
- Symmetry of digit sum differences \(\operatorname{sign}(S_5(k) - S_1(k))\)
- Step difference bound \(a(n+1) - a(n) \in \{1, 2\}\) in mass-redistribution cellular automata
- Sum of two squares and two central-binomial-type terms
- Sum of two squares, a power of 3, and a power of 5
- Maximality of \(k = 43\) with restricted digit counts in bases \(3 \le b < k\)
- The 2-4-6-8 Conjecture
- Vanishing of bases with \(b^n \equiv -1 \pmod{2n+1}\) for absolute Euler pseudoprimes
- Four-square conjecture with powers of 2, 3, and 5
- Characterization of Carmichael numbers via squarefree denominators \(a(n)\)
- Nonnegativity of the Dirichlet square root of A046644
- Pronic indices for odd coefficients of \(\sum_{n \ge 0} x^n \frac{(1+x^n)^n}{(1+x^{n+1})^{n+1}}\)
- Pronic indices for odd coefficients of \(\sum_{n \ge 0} x^n \frac{(1+x^n)^n}{(1-x^{n+1})^{n+1}}\)
- Tripling until the seed's digits reappear
- Convergence of fraction numerators \(a(n)/b(n)\) to \(e\)
- Bounds on fractional parts \(n r^2 - a(n)\) for \(r = (2+\sqrt{5})/2\)
- Numerator of a sum involving binomial coefficients
- Factor bounds for Fermat numbers
- A factorial ratio analogous to the Catalan numbers
- Primality of continued fraction denominators \(a(n)\) for \(n \ge 3\)
- Realization of primes \(p \equiv \pm 1 \pmod{10}\) by continued fraction denominators
A generating function with… to Non-Power-of-2 Almost Perfect…
- A generating function with powers two and three
- A generating function with powers two and four
- A generating function with powers two and four
- A quadratic generating function with sign substitution
- A generating function with signed square terms
- The generating function \(A(x)=1+3xA(x)^2-2xA(-x)^2\)
- Integrality of the factorial ratio \(\frac{(12n+6)! (6n+9)!}{108 (4n+2)! (2n+3)! ((6n+5)!)^2}\)
- Unique realization of odd primes \(p \notin \{3, 5\}\) by continued fraction values
- A cubic generating function with ternary substitution
- A logarithmic derivative with prime-divisible coefficients
- Periodicity of \(k\)-th prime factors in coupled nonlinear recurrence \(a(n)\)
- Lengths of the 2-dense sublists of divisors of \(n\)
- A differential generating function
- Maximum number of terms in a 2-dense sublist of divisors of \(n\)
- Decimal concatenation of a cofactor and the largest prime factor
- *abc* conjecture
- Agoh-Giuga conjecture
- Agrawal's conjecture
- Normality of Irrational Algebraic Numbers
- Non-Power-of-2 Almost Perfect Numbers Conjecture
Amicable numbers to Some conjectures about ranks of…
- Amicable numbers
- Andrica's conjecture
- Artin's conjecture on primitive roots
- Balanced prime conjecture
- Bateman-Horn Conjecture
- Beal conjecture
- Betrothed numbers
- Brocard's Conjecture
- Büchi's problem
- Bunyakovsky conjecture
- Carmichael's totient function conjecture
- Catalan's conjecture and related Diophantine equations
- Class number problem for real quadratic fields
- Collatz conjecture
- Congruent Number
- Dickson's conjecture
- Diophantine \(m\)-tuples
- Dirichlet divisor problem
- Elliott–Halberstam conjecture
- Some conjectures about ranks of elliptic curves over ℚ
Emirps to First Hardy–Littlewood…
- Emirps
- The Erdős–Moser equation
- Euclid Numbers conjecture
- Open questions regarding the existence of Euler bricks
- Euler's sum of powers conjecture
- Exponentials conjectures and theorems
- Factorial primes
- Feit-Thompson conjecture on primes
- Open questions about Fermat numbers
- Fermat-Catalan conjecture
- Fibonacci Primes
- Firoozbakht's conjecture
- Fortune's Conjecture
- Gauss circle problem
- Gilbreath's conjecture
- Goldbach's conjecture
- The Goormaghtigh conjecture
- Grimm's conjecture
- Hall's conjecture
- First Hardy–Littlewood conjecture
The Hasse--Weil conjecture for… to Oppermann's Conjecture
- The Hasse--Weil conjecture for elliptic curves
- Idoneal numbers completeness conjecture
- Open questions on irrationality of numbers
- Juggler conjecture
- Kummer–Vandiver conjecture
- Lander, Parkin, and Selfridge Conjecture
- Legendre's conjecture
- Lehmer's Mahler measure problem
- Lehmer's totient problem
- Lemoine's conjectures
- Littlewood conjectures
- Lonely runner conjecture
- Lychrel numbers in base 10
- Magic Squares
- Mahler's 3/2 Problem
- Conjectures about Mersenne primes
- Mills' Theorem
- Modularity conjecture
- Normality of mathematical constants
- Oppermann's Conjecture
Infinitude of Pell number primes to Sierpiński number
- Infinitude of Pell number primes
- Perfect numbers
- Pierpont primes
- Pollock's (tetrahedral numbers) conjecture
- Asymptotic density of powerful numbers
- Primes and perfect squares
- Prime Triplet Conjecture
- Quasiperfect Numbers
- Ramanujan τ-function
- Rational distance problem
- Infinite Regular Primes
- Decimal Repunit Primes
- Particular values of the Riemann zeta function
- Rudin's conjecture on squares in arithmetic progressions
- Sato–Tate conjecture
- Schanuel's Conjecture
- Hypothesis H
- Scholz conjecture on addition chains
- Selfridge's conjectures
- Sierpiński number
Singmaster's conjecture to Ben Green's Open Problem 14
- Singmaster's conjecture
- Solitary Numbers
- Sum of three cubes
- (m,k)-perfect numbers
- Tarski's exponential function problem
- Taxicab numbers
- Open questions on transcendence of numbers
- Twin prime conjecture
- Infinitude of Wall–Sun–Sun primes
- Can a prime \(p\) satisfy \(2^{p-1} \equiv 1 \pmod{p^2}\) and \(3^{p-1} \equiv 1 \pmod{p^2}\)?
- Wieferich primes
- Wilson primes
- Wolstenholme Prime
- Woodall Primes
- Ben Green's Open Problem 1
- Ben Green's Open Problem 2
- Ben Green's Open Problem 3
- Ben Green's Open Problem 7
- Green's Open Problem 12
- Ben Green's Open Problem 14
Green's Open Problem 15 to Ben Green's Open Problem 46
- Green's Open Problem 15
- Ben Green's Open Problem 16
- Ben Green's Open Problem 18
- Ben Green's Open Problem 19
- Ben Green's Open Problem 21
- Green's Open Problem 22
- Green's Open Problem 23
- Green's Open Problem 24
- Green's Open Problem 25
- Green's Open Problem 26
- Green's Open Problem 27
- Ben Green's Open Problem 31
- Green's Open Problem 32
- Ben Green's Open Problem 33
- Ben Green's Open Problem 37
- Green's Open Problem 38
- Ben Green's Open Problem 43
- Green's Open Problem 44
- Ben Green's Open Problem 45
- Ben Green's Open Problem 46
Green's Open Problem 47 to Kaplansky's problem on the…
- Green's Open Problem 47
- Green's Open Problem 49
- Ben Green's Open Problem 50
- Green's Open Problem 51
- Green's Open Problem 52
- Green's Open Problem 53
- Ben Green's Open Problem 57
- Ben Green's Open Problem 58
- Ben Green's Open Problem 60
- Ben Green's Open Problem 61
- Ben Green's Open Problem 62
- Green's Open Problem 64
- Ben Green's Open Problem 65
- Ben Green's Open Problem 66
- Ben Green's Open Problem 82
- Ben Green's Open Problem 93
- The Catch-Up game and conjecture
- Dubner's conjecture
- Gourevitch's series identity
- Kaplansky's problem on the values of the \(u\)-invariant
Kurepa's conjecture to Minimum modulus for the unique…
- Kurepa's conjecture
- Parities of partition numbers
- Pfister's problem on the Pythagoras number of \(\mathbb{R}(X_1, \dots, X_n)\)
- Prime Tuples Conjecture
- Equivalents to the Riemann Hypothesis
- Moments of the Riemann zeta function on the critical line
- Simple zeros of the Riemann zeta function on the critical line
- Serre's uniformity conjecture over the rationals
- Tu-Deng Conjecture
- Zagier's Conjecture on Multiple Zeta Values
- The Curling Number Conjecture
- Cunningham chains — Jones's conjecture
- Conway's subprime Fibonacci sequences
- Unique Crystal Components
- Barker sequences
- Digit \(2\) in base \(3\) representation of \(2^n\)
- An Arithmetic Sum Associated with the Classical Theta Function
- A conjecture by Margulis on matrix groups
- Integer values of \(\tan(\arctan 1 + \arctan 2 + \cdots + \arctan n)\)
- Minimum modulus for the unique multiset-sum problem
Mathoverflow 17560 to Tao's Optimization constant 1a…
- Mathoverflow 17560
- Mathoverflow 75792
- Are prime numbers among sums of prime numbers distributed as \(\frac n{2\ln(n)}\)?
- Bugeaud Collection of Conjectures and Open Questions: Fractional Parts of Powers
- Normal and rich numbers and the sequence \((b^n \xi)\) modulo one
- Bugeaud Collection of Conjectures and Open Questions: Spectrum of Sequence
- Bugeaud Collection of Conjectures and Open Questions: Lacunary Sequences in Real Number Fields
- Bugeaud Collection of Conjectures and Open Questions: Rapidly Increasing Sequences Dense Modulo One
- Bugeaud Collection of Conjectures and Open Questions: Confined Powers of Non-Pisot Numbers
- Bugeaud Collection of Conjectures and Open Questions: \(p\)-adic Littlewood Conjecture
- Bugeaud Collection of Conjectures and Open Questions: Mahler's Z-numbers
- Bugeaud Collection of Conjectures and Open Questions: Automatic Expansions in Two Bases
- Bugeaud Collection of Conjectures and Open Questions: Simultaneously Small Entropies
- Bugeaud Collection of Conjectures and Open Questions: Pisot orbits on the Cantor set
- Equidistributed Sequences
- Beaver Math Olympiad (BMO)
- Smarandache–Wellin primes
- The Birch and Swinnerton-Dyer (BSD) Conjecture
- Riemann Hypothesis and its generalizations
- Tao's Optimization constant 1a / An autocorrelation constant related to Sidon sets
Tao's Optimization Constant 7a… to Lam--Litt conjecture
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