Let n and r be positive integers with n ≥ r.
57418
How to prove this statement: $\binom{r}{r}+\binom{r+1}{r}+\cdots+\binom{n}{r}=\binom{n+1}{r+1}$
143067
Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.
112182
Sequence of positive integers such that their reciprocals are in arithmetic progression
3599
show that if ${a_n} \to a$, and $a>0$, then $\exists N$ such that $a_n>0$ for $n \ge N$.
149489
30 positive integers
114404
For which positive integer values of $n$ does $a|mn-b?$
72672
Show that if $ar + bs = 1$ for some $r$ and $s$ then $a$ and $b$ are relatively prime
63931
When $ab/(a+b)$ is an integer, where $a,b$ are positive integers.
122156
An inequality concerning three positive numbers
37569
Prove that $\binom{n}{r} + \binom{n}{r+1} = \binom{n+1}{r+1} $
46039
Prove that if $x \in R,$ then there exists $n \in Z$ satisfying $x \leq n < x+1$
121700
If $a$ and $b$ are positive real numbers, then $a + b \geq 2 \sqrt{ab}$.
51555
Strictly increasing sequence $\{ a_k \}$ of positive integers such that $\sum 1/{a_k}$ is finite
119046
Expressing a positive integer as a sum of positive integers
80827
Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
137750
Let $(a_n)$ be a strictly increasing sequence of positive integers such that: $a_2 = 2$, $a_{mn} = a_m a_n$ for $m, n$ relatively prime.
54430
For $a,b$ coprime, there exists positive integers $x,y$ such that $ax-by=1$