New posts in diophantine-equations

Values of $a$ such that $x^5-x-a$ has quadratic factor

elementary-number-theory diophantine-equations factoring

Positive integers satisfying $x^{a+b} = a^b \cdot b$, how to show that $a=x$ and $b=x^x$?

number-theory diophantine-equations

Local solutions of a Diophantine equation

number-theory diophantine-equations p-adic-number-theory

Does the sum of the reciprocals of composites that are $ \le $ 1

sequences-and-series elementary-number-theory diophantine-equations fractions

How to solve in integers the equation, $(x^2-y^2)^2=1+16y$?

algebra-precalculus diophantine-equations

Diophantine equation $(x+y)(x+y+1) - kxy = 0$

number-theory elementary-number-theory diophantine-equations vieta-jumping

What are the positive integer solutions to $x^2-x+1 = y^3$?

number-theory diophantine-equations elliptic-curves eisenstein-integers

Find all solutions of ${\frac {1} {x} } + {\frac {1} {y} } +{\frac {1} {z}}=1$, where $x$, $y$ and $z$ are positive integers

elementary-number-theory diophantine-equations

Solve equation $ 1+2^x=3^y$

diophantine-equations

Find $(a,b)$ if $x^2-bx+a = 0, x^2-ax+b = 0$ both have distinct positive integers roots

algebra-precalculus number-theory elementary-number-theory diophantine-equations quadratics

Integer solutions to $ n^2 + 1 = 2 \times 5^m$

diophantine-equations

Number of positive integral solutions of equation $\dfrac 1 x+ \dfrac 1 y= \dfrac 1 {n!}$

number-theory diophantine-equations

Solving $x^p + y^p = p^z$ in positive integers $x,y,z$ and a prime $p$

elementary-number-theory diophantine-equations

Proof that $x^2+4xy+y^2=1$ has infinitely many integer solutions

elementary-number-theory diophantine-equations

Integer solution of $abc=a+b+c+2$.

elementary-number-theory inequality diophantine-equations

On the equation $3x^3 + 4y^3 + 5z^3 = 0$

number-theory diophantine-equations

Showing a polynomial having at least one integer root under certain conditions has precisely one integer root [closed]

polynomials diophantine-equations

Divisibility of $2^n - 1$ by $2^{m+n} - 3^m$.

diophantine-equations divisibility collatz-conjecture

Determine if a number is the sum of two triangular numbers.

elementary-number-theory diophantine-equations

Primes as quotients

number-theory prime-numbers diophantine-equations