To derive quantity $k=\frac{2-p^2}{p+2}$ for positive rational $p$ such that $p^2>2$ and $(p+k)^2>2$
4552
Choice of $q$ in Baby Rudin's Example 1.1
118517
Does this constitute a valid proof that $\frac{x^2}{1+x^4} \leq \frac{1}{2}$?
63129
Infinite number of $k$ satisfying $p_{k+1} - p_{k} > 2$?
88036
Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$
145578
How find the value $\beta$ such $\left|\frac{p}{q}-\sqrt{2}\right|<\frac{\beta}{q^2}$
89590
The number of solutions of $ax^2+by^2\equiv 1\pmod{p}$ is $ p-\left(\frac{-ab}{p}\right)$
79950
Prove that for an integer n larger than or equal to 2, the period for the decimal expression of the rational number $\frac{1}{n}$ is at most n -1.
91101
Proving $\sqrt2$ is irrational
18285
Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$
145884
Showing $\left|\frac{a+b}{2}\right|^p+\left|\frac{a-b}{2}\right|^p\leq\frac{1}{2}|a|^p+\frac{1}{2}|b|^p$
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
94119
Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$
63409
If $x^2+ax+b=0$ has a rational root, show that it is in fact an integer
82016
Given $p^2+q^2+r^2+1=s+\sqrt{p+q+r-s}$, solve for $s$
115004
If $x\notin\mathbb Q$, then $\left|x-\frac{p}{q}\right|<\frac{1}{q^2}$ for infinitely many $\frac{p}{q}$?
11693
If $p \mid m^p+n^p$ prove $p^2 \mid m^p+n^p$
83407
How to show that that $q \mid p-1$?