If $p,q$ are prime, solve $p^3-q^5=(p+q)^2$.
87282
Diophantine equation involving prime numbers : $p^3 - q^5 = (p+q)^2$
43219
If $[K(\alpha):K]=p\neq q=[K(\beta):K]$ then $[K(\alpha+\beta):K]=pq$
140948
Suppose $p$ and $q$ are odd primes and $p = q + 4a$ for some $a$. Prove that $(\frac ap) = (\frac aq)$ holds.
76282
Prime number expressible as $2^2+3^3+5^5+7^7+11^{11}+\cdots$
43567
Some hints for "If a prime $p = n^2+5$, then $p\equiv 1\mod 10$ or $p\equiv 9\mod 10$"
21874
Solve $x^3+x \equiv 1 \pmod p$
139755
Prove that $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational. Generalise this.
34192
Solve $x^{5} \equiv 2$ mod $221\ $ [Taking modular $k$'th roots if unique]
37219
Quadratic Integers in $\mathbb Q[\sqrt{-5}]$
111967
Let $p$ be a prime number. Prove that there exists $x∈Z$ for which $p|x^2−x+ 3$ if and only if there exists $y∈Z$ for which $p|y^2−y+ 25$.
129521
Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
85042
Write $1/1 + 1/2 + ...1/ (p-1)=a/b$ with $(a,b)=1$. Show that $p^2 \mid a$ if $p\geq 5$ is prime [Wolstenholme's theorem]
58182
How to prove that $\mathbb{Q}[\sqrt{p_1}, \sqrt{p_2}, \ldots,\sqrt{p_n} ] = \mathbb{Q}[\sqrt{p_1}+ \sqrt{p_2}+\cdots + \sqrt{p_n}]$, for $p_i$ prime?
144765
Solving $\sqrt{x+5} = x - 1$
134885
proving that $\mathbb{Q}(\sqrt{5}, \sqrt{6}) = \mathbb{Q}(\sqrt{5}+ \sqrt{6}) $
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$
144814
If $p$ and $q$ are primes, which binomial coefficients $\binom{pq}{n}$ are divisible by $pq$?