New posts in conjectures

Conjecture about distribution of certain primes

number-theory prime-numbers conjectures

On the inequality $I(q^k)+I(n^2) \leq \frac{3q^{2k} + 2q^k + 1}{q^k (q^k + 1)}$ where $q^k n^2$ is an odd perfect number

upper-lower-bounds conjectures divisor-sum arithmetic-functions perfect-numbers

If $a+b+c$ divides the product $abc$, then is $(a,b,c)$ a Pythagorean Triple?

geometry proof-writing triangles conjectures pythagorean-triples

Euler's totient and divisors count function relationship when $[(\frac{\varphi(n)}{2}+1)\cdot(\frac{\tau(n)}{2}+1)] = n$

elementary-number-theory totient-function conjectures multiplicative-function divisor-counting-function

a conjecture of certain q-continued fractions

number-theory continued-fractions conjectures q-series

Conjectured continued fraction formula for Catalan's constant

sequences-and-series number-theory elementary-number-theory conjectures continued-fractions

Is $X = (n-1)^n + n$ always composite for $n \geq 4 \in \Bbb Z$?

elementary-number-theory modular-arithmetic conjectures

Is this known about $\pi$?

irrational-numbers pi conjectures

A Matrix With Eigenvalues Equal to The Golden Ratio and the Golden Conjugate

linear-algebra abstract-algebra eigenvalues-eigenvectors conjectures golden-ratio

Conjecture $\sum_{m=1}^\infty\frac{y_{n+1,m}y_{n,k}}{[y_{n+1,m}-y_{n,k}]^3}\overset{?}=\frac{n+1}{8}$, where $y_{n,k}=(\text{BesselJZero[n,k]})^2$

sequences-and-series special-functions closed-form bessel-functions conjectures

Analog of Cramer's conjecture for primes in a residue class

number-theory prime-numbers conjectures prime-gaps

Zhang's theorem and Polignac's conjecture

number-theory prime-numbers conjectures open-problem prime-twins

Prove that $\lim_{n\rightarrow \infty} \frac{\log_{10}\lfloor\text{Denominator of } H_{10^n}\rfloor+1 }{10^n}=\log_{10} e$

limits conjectures open-problem harmonic-numbers

Integral $\int_0^\infty\Big[\log\left(1+x^2\right)-\psi\left(1+x^2\right)\Big]dx$

integration definite-integrals closed-form conjectures polygamma

Does the Rogers-Ramanujan continued fraction $R(q)$ satisfy this conjectured infinite series

number-theory continued-fractions modular-forms conjectures q-series

How to show an infinite number of algebraic numbers $\alpha$ and $\beta$ for $_2F_1\left(\frac14,\frac14;\frac34;-\alpha\right)=\beta\,$?

calculus definite-integrals radicals hypergeometric-function conjectures

Prove that $\int_0^\infty\left(\arctan \frac1x\right)^2 \mathrm d x = \pi\ln 2$

calculus integration improper-integrals conjectures experimental-mathematics

how to prove this extended prime number theorem?

number-theory prime-numbers analytic-number-theory conjectures

Big-Daddy-Conjectures and Hierarchy of Mathematical Conjectures

number-theory big-list conjectures

Conjecture $\sum_{n=1}^\infty\frac{n^2}{(-1)^n \cosh(\pi n\sqrt{3})-1}=\frac{1}{12\pi^2}$

calculus sequences-and-series closed-form conjectures