Using the fundamental theorem of arithmetic to prove $\sqrt{\text{prime}}\not\in\Bbb Q$
53945
The square root of a prime number is irrational
154305
Let $\pi$ denote a prime element in $\mathbb Z[i], \pi \notin \mathbb Z, i \mathbb Z$. Prove that $N(\pi)=2$ or $N(\pi)=p$, $p \equiv 1 \pmod 4$
140194
Using natural deduction to prove that $p \implies q \vdash \lnot p \lor q$
77240
Show that $4 + \sqrt{10}$ is not prime in $\mathbb{Z}\bigl [\sqrt{10}\bigr]$
130244
Exercise similar to prime avoidance theorem in R.Y. Sharp's textbook
3632
Basic number theory proofs
106157
Proof of Euclid's lemma using fundamental theorem of arithmetic
63702
There is a prime between $n$ and $n^2$, without Bertrand
87682
Show that $\sqrt{2}\notin \mathbb{Q}(\sqrt[4]{3})$
144592
how to prove the existence and uniqueness of the prime factorization of any natural number.
24444
Prove that $371\cdots 1$ is not prime
44600
How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
81221
The prime number theorem over a finite field - Lang's *Algebra*, Chapter V, Exercise 23(b)
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
134885
proving that $\mathbb{Q}(\sqrt{5}, \sqrt{6}) = \mathbb{Q}(\sqrt{5}+ \sqrt{6}) $
136947
Simple Mersenne prime divisibility proofs
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$