For every $n \in \Bbb Z$, prove there exists $a, b \in \Bbb Z$ such that $n = 5a + 2b$
43010
Prove that for every n ∈ Z, there exist a, b ∈ Z such that $n = 5a + 2b$.
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
31766
Prove that $a_{n}=0$ for all $n$, if $\sum a_{kn}=0$ for all $k\geq 1$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
133382
Proof that $a+b+\frac{1}{1+\sqrt{ab}}\geq\frac{5}{2}$
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
131754
Prove $ \forall c \in \mathbb{R^{+}}, \forall B \in \mathbb{N}, \exists n \in \mathbb{N}, (n \geq B) \wedge (\sqrt{2n} > c \ln(n+2)) $?
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
114185
Existence of $x$ such that $2^x =a,3^x=b,5^x=c$ for some integers $a,b,c$
77448
$n\ge 8\,\Rightarrow\, n = 3j + 5k\ $ for $\,j,k,n\in \Bbb N$
46039
Prove that if $x \in R,$ then there exists $n \in Z$ satisfying $x \leq n < x+1$
149661
For $n=pq$, show that there exist $\alpha, \beta \in Z_n^*$ such that $\alpha, \beta \notin (Z_n^*)^2$ and $\alpha \cdot \beta \notin (Z_n^*)^2$.
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
133017
Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$