Newbetuts

Generalizing the sum of consecutive cubes $\sum_{k=1}^n k^3 = \Big(\sum_{k=1}^n k\Big)^2$ to other odd powers

Rational solutions to $a+b+c=abc=6$

An integer is an $n$th power if that holds true for all moduli

$|2^x-3^y|=1$ has only three natural pairs as solutions

$x^2+y^2=z^n$: Find solutions without Pythagoras!

Finding triplets $(a,b,c)$ such that $\sqrt{abc}\in\mathbb N$ divides $(a-1)(b-1)(c-1)$

Find all integer solutions for the equation $|5x^2 - y^2| = 4$

Golden Number Theory

To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$

On Ramanujan's curious equality for $\sqrt{2\,(1-3^{-2})(1-7^{-2})(1-11^{-2})\cdots} $

Let $k$ be a natural number . Then $3k+1$ , $4k+1$ and $6k+1$ cannot all be square numbers.

Integral solutions of $x^2+y^2+1=z^2$

$n!+1$ being a perfect square

Parametrization of solutions of diophantine equation

New posts in diophantine-equations

Is $\sqrt[3]{p+q\sqrt{3}}+\sqrt[3]{p-q\sqrt{3}}=n$, $(p,q,n)\in\mathbb{N} ^3$ solvable?

Can $n!$ be a perfect square when $n$ is an integer greater than $1$?

Decomposing polynomials with integer coefficients

Number of solution for $xy +yz + zx = N$

Solutions to $y^2 = x^3 + k$?

Generate solutions of Quadratic Diophantine Equation

Generalizing the sum of consecutive cubes $\sum_{k=1}^n k^3 = \Big(\sum_{k=1}^n k\Big)^2$ to other odd powers

Rational solutions to $a+b+c=abc=6$

An integer is an $n$th power if that holds true for all moduli

$|2^x-3^y|=1$ has only three natural pairs as solutions

$x^2+y^2=z^n$: Find solutions without Pythagoras!

Finding triplets $(a,b,c)$ such that $\sqrt{abc}\in\mathbb N$ divides $(a-1)(b-1)(c-1)$

Find all integer solutions for the equation $|5x^2 - y^2| = 4$

Golden Number Theory

To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$

On Ramanujan's curious equality for $\sqrt{2\,(1-3^{-2})(1-7^{-2})(1-11^{-2})\cdots} $

Let $k$ be a natural number . Then $3k+1$ , $4k+1$ and $6k+1$ cannot all be square numbers.

Integral solutions of $x^2+y^2+1=z^2$

$n!+1$ being a perfect square

Parametrization of solutions of diophantine equation