Prove that there is no positive rational number a such that $a^2 = 3$.
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
23427
How to prove there are no more positive integers that are products of 2 and 3 consecutive numbers?
99311
Prove $2^{1/3} + 2^{2/3}$ is irrational
81377
Show that $x^n + x + 3$ is irreducible for all $n \geq 2.$
86378
Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$
41486
If $x^n + a_{n-1}x^{n-1} + ... + a_0 = 0$ has a rational root, then such root is an integer
126427
Proving $\sqrt{2}+\sqrt[3]{3}$ is algebraic.
69575
If $ad$ and $bc$ are odd and even, respectively, then prove that $ax^3+bx^2+cx+d$ has an irrational root.
126494
Prove that there doesn't exist any integer $x \ge 3$ such that $x^2-1$ is prime.
56877
Show that $\sqrt{4 + 2\sqrt{3}} - \sqrt{3}$ is rational.
31744
Proving that there is an irrational number between any two unequal rational numbers.
30478
How to prove that a number 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.
28274
Prove that $x^2 + y^2 = 3(z^2 + m^2)$ has no solutions in integer
105405
Product of three consecutive positive integers is never a perfect power
44309
Prove $5a^2 ≠ 3b^2$ for all non-zero rational numbers $a$ and $b$
153532
Proving $a^2$ is even $\implies$ $a$ is even by contradiction