Find all positive integers $a, b, c$ such that $a^2+1$ and $b^2+1$ are both primes and $(a^2+1)(b^2+1)=c^2+1$
70406
Find all values x, y and z which satisfy the equation $(x^2 + 1)(y^2 + 1) = z^2 + 1$ given that $(x^2 + 1)$ and $(y^2 + 1)$ are both primes.
106030
Find all the positive integer
50663
prove or disprove: For a prime number p, there is a positive integer n such that $p+1 $= $n^2$ if and only if $ p = 3.$
134857
Find $(a,b)$ if $x^2-bx+a = 0, x^2-ax+b = 0$ both have distinct positive integers roots
142133
Prove that if $a^2 + b^2 = c^2$, then 5 divides abc. a,b,c are positive integers.
54430
For $a,b$ coprime, there exists positive integers $x,y$ such that $ax-by=1$
31257
Let $a,b,c>0$ such that $a+b+c=3$, find max/min of $\frac1{a^2+1}+\frac1{b^2+1}+\frac1{c^2+1}$
72389
Positive integer $n$ such that $2n+1$ , $3n+1$ are both perfect squares
56328
Find p is the prime number which $\frac{p+1}{2}$ and $\frac{p^2+1}{2}$ both are square number.
137230
Find all pairs of primes $p,q$ such that $pq \mid 2^p +2^q$
69582
Is it true that: $a+bi$ is prime in $\mathbb{Z}[i]$ if and only if $a^2+b^2$ is prime in $\mathbb{Z}$
58114
For which primes p is $p^2 + 2$ also prime?
45356
Are there any positive integers $a, b, c, d$ such that both $(a, b, c)$ and $(b, c, d)$ are Pythagorean triples?
104920
Can we find positive integers $a$ and $k \geq 2$ with $2^n - 1 = a^k$?
75011
Primes of the form $n^2+1$ - hard?
137626
If $a,b,c$ are positive integers,and $\cfrac{a}{b}+\cfrac{b}{c}+\cfrac{c}{a}$ and $\cfrac{b}{a}+\cfrac{c}{b}+\cfrac{a}{c}$ are integers then $a=b=c$
115244
Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$