If $z | 5x+11y$ and $z | 6x+13y$, then $z | y$.
25825
Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
49209
Prove $(x+y)(y+z)(x+z)≤\frac8{27}(x+y+z)^3$
34693
Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
42516
If every $x\in X$ is uniquely $x=y+z$ then $\|z\|+\|y\|\leq C\|x\|$
86211
If $x+y+z \geq xyz$ Prove that $x^2 + y^2 + z^2 \geq xyz$.
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
97667
If $a<b$, $c<d$ then $a+c<b+d$?
25784
Let $x$ and $y$ be positive integers such that $xy \mid x^2+y^2+1$.
158551
If $X \perp Y$ and $X+Y \in L^1$ then $X,Y \in L^1$
43219
If $[K(\alpha):K]=p\neq q=[K(\beta):K]$ then $[K(\alpha+\beta):K]=pq$
142724
Prove that for all integers $x$ and $y$, $x - y$ is odd if and only if $x + y$ is odd.
46547
System of equations: $x^2+y=7, y^2+x=11$
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
102175
$Z=XY$, $E_Z[Z]$, $E_{X,Y}[XY]$
120292
How to formally prove: if $d\mid da+b$, then $d\mid b$?
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$