New posts in diophantine-equations

Did Lagrange and/or Lebesgue and/or Lucas solve Ljunggren's equation?

elementary-number-theory proof-verification reference-request diophantine-equations

Find all solutions to $h \pm \sqrt{h^2 - 671} \in \mathbb{Z}$

number-theory elementary-number-theory diophantine-equations

Can we find positive integers $a$ and $k \geq 2$ with $2^n - 1 = a^k$? [closed]

elementary-number-theory diophantine-equations

Determine if $x^3+y^3+z^3+t^3 = 10^{2021}$ has a solution

diophantine-equations mathematica

When is $\sqrt[3]{a+\sqrt b}+\sqrt[3]{a-\sqrt b}$ an integer? [duplicate]

polynomials diophantine-equations radicals

Four squares such that the difference of any two is a square?

number-theory systems-of-equations diophantine-equations pythagorean-triples

Does the equation $y^2=3x^4-3x^2+1$ have an elementary solution?

elementary-number-theory diophantine-equations infinite-descent

More elliptic curves for $x^4+y^4+z^4 = 1$?

number-theory diophantine-equations elliptic-curves

Integers can be expressed as $a^3+b^3+c^3-3abc$

number-theory elementary-number-theory diophantine-equations

Diophantine equation: $7^x=3^y-2$

elementary-number-theory diophantine-equations

Let $k$ be a postive integer number . Then $2k^2+1$ and $3k^2+1$ cannot both be square numbers.

number-theory diophantine-equations pell-type-equations

General quadratic diophantine equation.

algebraic-geometry diophantine-equations conic-sections

Solving the following Diophantine equation: $m^2=n^5-5$

number-theory diophantine-equations

A System of Simultaneous Pell Equations

number-theory diophantine-equations pell-type-equations

All positive integer solutions to $\frac{1}{x_1}+\frac{1}{x_2}+\cdots+\frac{1}{x_n}+\frac{1}{x_1 x_2 \cdots x_n}=1$

diophantine-equations number-theory

For integers $x<y<z$, why are these cases impossible for Mengoli's Six-Square Problem?

diophantine-equations square-numbers sums-of-squares pythagorean-triples elementary-number-theory

$x^4+y^4=2z^2$ has only solution, $x=y=z=1$ .

elementary-number-theory diophantine-equations

prove that $x^2 + y^2 = z^4$ has infinitely many solutions with $(x,y,z)=1$

number-theory diophantine-equations

Can a parallelogram have whole-number lengths for all four sides and both diagonals?

geometry elementary-number-theory diophantine-equations polygons

Find all primes $p$ such that $ p^3-4p+9 $ is a perfect square.

number-theory diophantine-equations