New posts in conjectures

Prove that $\sum\limits_{i=1}^{n} a_i\geq n^2$.

number-theory discrete-mathematics conjectures

open conjectures in real analysis targeting real valued functions of a single real variable

real-analysis soft-question big-list conjectures

A conjectured identity for tetralogarithms $\operatorname{Li}_4$

logarithms special-functions closed-form conjectures polylogarithm

An inequality involving three consecutive primes

elementary-number-theory inequality prime-numbers examples-counterexamples conjectures

conjectured general continued fraction for the quotient of gamma functions

number-theory gamma-function continued-fractions conjectures

Every prime number divide some sum of the first $k$ primes.

prime-numbers divisibility conjectures

Twin, cousin, sexy, ... primes

number-theory prime-numbers conjectures

Continuous Collatz Conjecture

conjectures collatz-conjecture

List of generally believed conjectures which cannot all be true

soft-question conjectures

Closed form for $\int_{-1}^1\frac{\ln\left(2+x\,\sqrt3\right)}{\sqrt{1-x^2}\,\left(2+x\,\sqrt3\right)^n}dx$

calculus definite-integrals closed-form conjectures hypergeometric-function

Conjecture $\Re\,\operatorname{Li}_2\left(\frac12+\frac i6\right)=\frac{7\pi^2}{48}-\frac13\arctan^22-\frac16\arctan^23-\frac18\ln^2(\tfrac{18}5)$

calculus complex-analysis closed-form conjectures polylogarithm

Subsubgroups are subgroups of subgroups / Multiplicative Property of the Index

abstract-algebra group-theory proof-verification conjectures

Euler's Totient function $\forall n\ge3$, if $(\frac{\varphi(n)}{2}+1)\ \mid\ n\ $ then $\frac{\varphi(n)}{2}+1$ is prime

elementary-number-theory prime-numbers totient-function conjectures multiplicative-function

An integral $\int_0^\infty P_s(x-1)\,e^{-x}\,dx$ involving Legendre functions

calculus integration special-functions conjectures hypergeometric-function

How to prove $4\times{_2F_1}(-1/4,3/4;7/4;(2-\sqrt3)/4)-{_2F_1}(3/4,3/4;7/4;(2-\sqrt3)/4)\stackrel?=\frac{3\sqrt[4]{2+\sqrt3}}{\sqrt2}$

calculus special-functions closed-form conjectures hypergeometric-function

Prove that there are no composite integers $n=am+1$ such that $m \ | \ \phi(n)$

number-theory elementary-number-theory prime-numbers totient-function conjectures

Status of a conjecture about powers of 2

number-theory open-problem conjectures

A conjectured value for $\operatorname{Re} \operatorname{Li}_4 (1 + i)$

integration closed-form conjectures polylogarithm

Simplify $\frac{_3F_2\left(\frac{1}{2},\frac{3}{4},\frac{5}{4};1,\frac{3}{2};\frac{3}{4}\right)}{\Pi\left(\frac{1}{4}\big|\frac{1}{\sqrt{3}}\right)}$

calculus closed-form conjectures hypergeometric-function elliptic-integrals

Is $K\left(\frac{\sqrt{2-\sqrt3}}2\right)\stackrel?=\frac{\Gamma\left(\frac16\right)\Gamma\left(\frac13\right)}{4\ \sqrt[4]3\ \sqrt\pi}$

calculus special-functions gamma-function closed-form conjectures