New posts in Diophantine Equations

Can $\frac{a^4}{b^3}$ be arbitary close to $1$?

Integer solutions to $y^{2} = 2x^{2} +15x$.

How to solve the diophantine equation $2(x+y)=xy+9$?

Is there an elementary proof that $y^2=8x^4+1$ has no integral solution for $x\ge2$?

Solve in positive integers $\sqrt{n+1982^n}+\sqrt n=(\sqrt{1983}+1)^k$

Does there exist $a \in \mathbb{Q}$ such that $a^2 - a + 1$ is a square?

Does the equation $a^{2} + b^{7} + c^{13} + d^{14} = e^{15}$ have a solution in positive integers

What are the solutions to $a^2+ab+b^2$ $=$ $3^n$?

Can both $n+3\; \text{and}\; n^2+3$ both be cubic numbers at same time?

Find all prime solutions of equation $5x^2-7x+1=y^2.$