Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too
66216
Squares, Cubes and Prime numbers
54286
Let $p$ a prime number, then prove that : $\sum \limits_{k=0}^{p} \binom {p}{k} \binom{p+k}{k} \equiv 2^p +1 \pmod{p^2}$
115726
For $p,q$ prime and $p \neq q$ show that $C_p \times C_q \cong C_{pq}$
127816
Number theory proof mod p
148713
If $p\geq 5$ is a prime number, show that $p^2+2$ is composite.
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
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.$
135586
Prove that the preimage of a prime ideal is also prime.
52530
There exists a prime congruent to $m$ mod $p$
834
If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.
83721
If a prime $p\mid ab$, then $p\mid a$ or $p\mid b\ $ [Euclid's Lemma]
90144
Show that if $a+bi$ is irreducible over $\mathbb{Z} [i]$ then $a^2 + b^2$ is prime over $\mathbb{Z} $
48691
Product of all prime numbers upto some prime $p$
149747
Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
141418
When is $\mathbb{F}_p[x]/(x^2-2)\simeq\mathbb{F}_p[x]/(x^2-3)$ for small primes?
86594
If $x^2 \equiv y^2 \pmod {p^r}$, where $p$ is an odd prime not dividing $x$ or $y$ then $x \equiv \pm y \pmod {p^r}$
50781
$(n+1)$th prime $p_{n+1}$ less than or equal to $p_1p_2\dots p_n+1$