List questions from vieta-jumping | MathQa

Find the integer values of c

Published on 12 Jan 2025 - 18:21

For which integers $a,b$ does $ab-1$ divide $a^3+1$?

Published on 12 Jan 2025 - 23:43

Find $n \in N$, for which $a+b+c+d = n \sqrt{(abcd)}$ has a solution $(a, b, c, d)$ in natural numbers.

Published on 28 Dec 2024 - 19:00

Find all natural solutions $(a, b)$ such that $(ab - 1) \mid (a^2 + a - 1)^2$.

Published on 12 Jan 2025 - 23:53

A generalization of the (in)famous IMO 1988 problem 6: If $\frac{a^2 + b^2 - abc}{ab + 1}$ is a positive integer then it is a square.

Published on 28 Dec 2024 - 16:18

Number Theory Problem Germany 2003

Published on 12 Jan 2025 - 23:34

Find all positive integer pairs $(a, b)$ such that $(ab + a + b) \mid (a^2 + b^2 + 1)$.

Published on 12 Jan 2025 - 23:56

Find all positive integers $n$ for which the equation $x + y + u + v = n \sqrt{ xyuv }$ has a solution in positive integers.

Published on 28 Dec 2024 - 5:59

All integer values of $\frac{a^2+b^2+1}{ab-1}$

Published on 12 Jan 2025 - 23:38

Find all positive integers which are representable uniquely as $\frac{x^2+y}{xy+1}$ with $x,y$ positive integers.

Published on 28 Dec 2024 - 22:52