$x^2+3y^2=p$ for p prime , has a solution $(x,y) \in \mathbb{Z^2}$ iff $ p \equiv 1$ (mod 3) .
42376
Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$
112390
Solutions of $x^2 \equiv 1 \pmod N$
33469
Diophantine equation $ax + by = c$ has an integer solution $x_0, y_0$ if and only if $\gcd(a,b)|c$
53503
Solving the diophantine equation $y^{2}=x^{3}-2$
21874
Solve $x^3+x \equiv 1 \pmod p$
95162
For a odd prime $p, \exists a,b$ such that $a^2 + ab + b^2 \equiv 0 \pmod{p} \iff \exists x,y $ such taht $x^2 + xy + y^2 = p$?
74214
Prove that there are $p+1$ points on the elliptic curve $y^2 = x^3 + 1$ over $\mathbb{F}_p$, where $p > 3$ is a prime such that $p \equiv 2 \pmod 3$.
99739
The diophantine equation $x^2+y^2=3z^2$
130846
Prove or disprove: If $a \in \mathbb{Z}$, $a > 0$, and $p$ is a prime such that $p^4 \mid a^3$, then $p^2 \mid a$.
123159
Solutions of the diophantine equation $x+y+z=xyz$?
69874
Are there any integer solutions to $a^3=b^2$?
22112
Find all integer solutions to $x^2+4=y^3$.
139
Prove or disprove: For every integer a, if a is not congruent to 0 (mod 3), the a^2 is congruent to 1 (mod 3)
21629
Using Fermat's Little Theorem Prove if $p$ is prime, prove $1^p + 2^p + 3^p +...+(p-1)^p \equiv 0 \bmod{p}$
44033
Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$
145287
Solve for integers $x, y, z$ such that $x + y = 1 - z$ and $x^3 + y^3 = 1 - z^2$.
23099
Verifying that the ideal $(x^3-y^2)$ is prime