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individ
  • Member for 10 years, 4 months
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12 votes
Accepted

If $n = a^2 + b^2 + c^2$ for positive integers $a$, $b$,$c$, show that there exist positive integers $x$, $y$, $z$ such that $n^2 = x^2 + y^2 + z^2$.

10 votes

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

8 votes

How to find all rational solutions of $\ x^2 + 3y^2 = 7 $?

7 votes

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

6 votes

Integer solutions for $\frac{1}{x^2}+\frac{1}{y^2}=\frac{1}{z^2}$?

6 votes

Find all integers satisfying $m^2=n_1^2+n_1n_2+n_2^2$

5 votes
Accepted

When is the sum of two squares the sum of two cubes

5 votes

Solutions to $ax^2 + by^2 = cz^2$

5 votes

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

4 votes

The equation $a^3 + b^3 = c^2$ has solution $(a, b, c) = (2,2,4)$.

4 votes

Help solving $ax^2+by^2+cz^2+dxy+exz+fzy=0$ where $(x_0,y_0,z_0)$ is a known integral solution

4 votes

The diophantine equation $a^2+ab-b^2=0$

3 votes

Erdős-Straus conjecture

3 votes

Find all integer solutions to Diophantine equation $x^3+y^3+z^3=w^3$

3 votes

Variation of Pythagorean triplets: $x^2+y^2 = z^3$

3 votes

How to find integer solutions to $M^2=5N^2+2N+1$?

3 votes

Does $8a+5$ ever divide $b^2+8$?

3 votes

Can we predict when a polynomial can take more than one perfect square value?

3 votes

Parametrization of solutions of diophantine equation

3 votes
Accepted

Biggest set such that sum of any pair is perfect square

3 votes

Solve $3x^2-y^2=2$ for Integers

3 votes

Pythagorean type diophantine equation.

3 votes

Pythagorean type diophantine equation.

3 votes

Ask for the rational roots of $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}=4.$

3 votes

Question about parametric divisibility relations

3 votes

Are there infinitely-many numbers that are both square and triangular?

3 votes

Given prime $p$, find solutions to $x^2 + p y^2 = z^3$

3 votes

Infinitely many $n$ such that $n, n+1, n+2$ are each the sum of two perfect squares.

3 votes

$(a^2+b^2)\cdot (c^2+d^2) = z^2+1$ then $z = ac+bd$ ?

3 votes
Accepted

$x^2+y^3 = z^4$ for positive integers

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