$x,y$ and $z$ are consecutive integers, $\frac {1}{x}+\frac {1}{y}+\frac {1}{z}$...
40635
Finding Maximum value of consecutive positive integers with constraints
82961
Show that $\left| \frac{1}{x}-\frac{1}{z} \right| \le \left|\frac{1}{x} - \frac{1}{y} \right| + \left|\frac{1}{y} - \frac{1}{z} \right|$.
93634
X,Y,Z independent and $\sim N(1,1)$. Find $P(X+Y \geqq 3Z)$
6595
Solve for positive integers: $\frac{4}{13}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$
73206
recursion-consecutive numbers
49209
Prove $(x+y)(y+z)(x+z)≤\frac8{27}(x+y+z)^3$
92290
For each $x,y,z∈\mathbb N$, if $x<y$ then $x+z<y+z$
24446
Prove that for each $n$, there exist $n$ consecutive integers, each of which is divisible by a perfect square larger than $1$.
62508
If $x$, $y$, $z$ are in arithmetic progression, show that $\frac{\sin x + \sin y + \sin z }{\cos x + \cos y + \cos z} = \tan y. $
125855
Prove: The product of any three consecutive integers is divisible by $6$.
120736
If xy + yz + zx = 1, ...........
45616
Find all solutions of ${\frac {1} {x} } + {\frac {1} {y} } +{\frac {1} {z}}=1$, where $x$, $y$ and $z$ are positive integers
139935
Show that any set of 7 distinct integers includes two integers $x$ and $y$, such that either $x-y$ or $x+y$ is divisible by 10
13072
If $x,y,z\gt 0$ and $xyz=1$ Then minimum value of $\frac{x^2}{y+z}+\frac{y^2}{z+x}+\frac{z^2}{x+y}$
33810
Proving there are an infinite number of pairs of positive integers $(m,n)$ such that $\frac{m+1}{n}+\frac{n+1}{m}$ is a positive integer
142076
$c$ is a complex number that satisyfing $(c+\frac{1}{c}+1)(c+\frac{1}{c}) = 1$
14815
How prove this $\prod_{1\le i<j\le n}\frac{a_{j}-a_{i}}{j-i}$ is integer