Prove that for any prime $p$ there is no rational number $a$ such that $a^2 = p$.
67031
use contradiction to prove that the square root of $p$ is irrational
140405
Show that there does not exist any $n$ for which $a^n=a$ forall $a\in \Bbb Z_m$ where $m$ is divisible by the square of some prime.
144851
For a prime $p \equiv 1$ or $3$ (mod $8$), show that the equation $x^{2} + 2y^{2} = p$ has a solution.
36943
How to prove that $L=${$a^p$: p is prime} isn't regular?
34588
Number Theory: $p!+p=n^2$, $p$ = prime
102234
Show $a^p \equiv a \mod 2p$
156940
There does not exist a polynomial $p(x)$ with integer coefficients which gives a prime number $\forall x\in \mathbb{Z}$
119180
How to prove that the set $A = \left\{ {p:{p^2} < 2,p \in {\Bbb Q^+}} \right\}$ has no greatest element?
74920
Prove that the equation $x^2-y^2 = 2002$ has no integer solution
69264
Is there an irrational number $a$ such that $a^a$ is rational?
96647
Number theory: Problem involving rational numbers
87764
Prove that the difference between two rational numbers is rational
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$
51649
prove there is no smallest positive rational number
140949
Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
94017
If p is a prime and a ∈Z. How do we prove that the congruence x^x ≡ a (mod p) is solvable?
108237
Show $a^p \equiv b^p \mod p^2$