New posts in diophantine-equations

Find all natural numbers $n > 1$ and $m > 1$ such that $1!3!5!\cdots(2n - 1)! = m!$

combinatorics number-theory diophantine-equations factorial

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

number-theory diophantine-equations

Can the determinant of an integer matrix with a given row be any multiple of the gcd of that row?

matrices number-theory diophantine-equations determinant gcd-and-lcm

Why can't the Alpertron solve this Pell-like equation?

elementary-number-theory diophantine-equations

Diophantine equation $ax + by = c$ has an integer solution $x_0, y_0$ if and only if $\gcd(a,b)|c$

elementary-number-theory discrete-mathematics diophantine-equations divisibility

Find all integer solutions of $1+x+x^2+x^3=y^2$

diophantine-equations

Solve $n(n+1)(n+2)=6m^3$ in positive integers

number-theory diophantine-equations

Integer solutions to $x^2-y^2=2^k$ [duplicate]

number-theory diophantine-equations

Solutions to Diophantine Equation $x^2 - D y^2 = m^2$

diophantine-equations

Finding all the numbers that fit $x! + y! = z!$

elementary-number-theory diophantine-equations factorial

Every natural number is representable as $\sum_{k=1}^{n} \pm k^5$ ... if somebody proves it for 240 integers

number-theory diophantine-equations

Integral solutions to $y^{2}=x^{3}-1$

number-theory algebraic-number-theory diophantine-equations

Prove that the equation $x^2-y^2 = 2002$ has no integer solution

elementary-number-theory diophantine-equations

Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?

elementary-number-theory diophantine-equations

What are all the integral solutions of $n!=m(m^2-1)$?

number-theory elementary-number-theory arithmetic diophantine-equations integers

Tricky positive diophantine equation

diophantine-equations

Is it possible that $(x+2)(x+1)x=3(y+2)(y+1)y$ for positive integers $x$ and $y$?

elementary-number-theory diophantine-equations

Failure of an elementary 'proof' of Fermat's Last Theorem?

number-theory proof-verification diophantine-equations fake-proofs

Are there integer solutions to $9^x - 8^y = 1$?

number-theory diophantine-equations

Find answer of $\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{y+x}=4$

number-theory diophantine-equations homogeneous-equation