For any positive integers p and q, prove that p + q ≤ 1 + pq
42446
Simple Elementary Algebra Equality
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
122326
Proving $|P(A\cap B)-P(A)P(B)|\leq \frac{1}4$
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
83752
If $p + q = 1$ prove that for any natural $n, m$ following is true: $(1 - p^n)^m + (1 - q^m)^n \ge 1$
142992
Prove that for every positive integer $n$, $1/1^2+1/2^2+1/3^2+\cdots+1/n^2\le2-1/n$
56624
Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers
114489
Solving $x^p + y^p = p^z$ in positive integers $x,y,z$ and a prime $p$
137511
Trying to show that $\sup \{b^p:p\in Q,\;0<p<x\} = \inf\{b^q:q\in Q,\;x<q\}$
102464
Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
66535
How to prove $P(A\cap B)\geqslant P(A)+P(B)-1$?
83407
How to show that that $q \mid p-1$?
19046
Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n
108704
Help with proof of $|x+y| \geq |x|-|y|$
29935
If $a, b, c, d>0$ and $abcd=1$ prove that an inequality holds true