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Does this system of simultaneous Pell-like equations have any non-trivial positive integer solutions?

How many integer solutions to a linear combination, with restrictions?

Do there exist an infinite number of integer-solutions $(x,y,z)$ of $x^x\cdot y^y=z^z$ where $1\lt x\le y$?

Find a solution: $3(x^2+y^2+z^2)=10(xy+yz+zx)$

Why can't prime numbers satisfy the Pythagoras Theorem? That is, why can't a set of 3 prime numbers be a Pythagorean triplet?

Diophantine Equations : Solving $a^2+ b^2=2c^2$

Proof that the equation $x^2 - 3y^2 = 1$ has infinite solutions for $x$ and $y$ being integers

Find all the integral solutions to $x^6-y^6+3x^4y-3y^4x+y^3+3x^2+3x+1=0$

Is there any integer solutions of $3x^3+3x+7=y^3$?

A curious coincidence for Wroblewski's solutions to $1^4+x_2^4+x_3^4+x_4^4+x_5^4 = y_1^4$

$x^3+48=y^4$ does not have integer (?) solutions

Finding all integer solutions of $5^x+7^y=2^z$

(Diophantine?) Equations With Multiple Variables

Chicken Problem from Terry Tao's blog (system of Diophantine equations)

Solutions to Diophantine Equations

New posts in diophantine-equations

$x^2+y^2=2z^2$, positive integer solutions

If $(m,n)\in\mathbb Z_+^2$ satisfies $3m^2+m = 4n^2+n$ then $(m-n)$ is a perfect square.

$x^2+y^2+z^2=5(xy+yz+zx)$ -- Is this all solutions?

Diophantine equation $x^4+5y^4=z^4$

Finding solutions to equation of the form $1+x+x^{2} + \cdots + x^{m} = y^{n}$

Does this system of simultaneous Pell-like equations have any non-trivial positive integer solutions?

How many integer solutions to a linear combination, with restrictions?

Do there exist an infinite number of integer-solutions $(x,y,z)$ of $x^x\cdot y^y=z^z$ where $1\lt x\le y$?

Find a solution: $3(x^2+y^2+z^2)=10(xy+yz+zx)$

Why can't prime numbers satisfy the Pythagoras Theorem? That is, why can't a set of 3 prime numbers be a Pythagorean triplet?

Diophantine Equations : Solving $a^2+ b^2=2c^2$

Proof that the equation $x^2 - 3y^2 = 1$ has infinite solutions for $x$ and $y$ being integers

Find all the integral solutions to $x^6-y^6+3x^4y-3y^4x+y^3+3x^2+3x+1=0$

Is there any integer solutions of $3x^3+3x+7=y^3$?

A curious coincidence for Wroblewski's solutions to $1^4+x_2^4+x_3^4+x_4^4+x_5^4 = y_1^4$

$x^3+48=y^4$ does not have integer (?) solutions

Finding all integer solutions of $5^x+7^y=2^z$

(Diophantine?) Equations With Multiple Variables

Chicken Problem from Terry Tao's blog (system of Diophantine equations)

Solutions to Diophantine Equations