Given a real $x$ and an integer $N \gt 1$, prove that there exist integers $h$ and $k$ with $0 \lt k \le N$ such that $|kx-h|\lt 1/N$.
124456
Given $x \in \mathbb{R}$ and $N \in \mathbb{N}, N>1,$ find integers $h,k$ with $0 < k \leq N $ that satisfy $\lvert{kx - h\rvert} < 1/N.$
41412
Inequality in number theory
36485
$H_n(X,A) \not \approx \tilde{H}_n(X/A)$
143067
Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
90199
Prove that there exists a constant $c>0$ such that the following happens
100234
Proving that $x^n$ converges to $0$ whenever $|x| < 1$
11586
Sequences of Real Numbers in a closed bounded interval
51555
Strictly increasing sequence $\{ a_k \}$ of positive integers such that $\sum 1/{a_k}$ is finite
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
102307
Discrete Math Proofs Involving Real Numbers
24446
Prove that for each $n$, there exist $n$ consecutive integers, each of which is divisible by a perfect square larger than $1$.
22154
Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
49372
$x+1/x$ an integer implies $x^n+1/x^n$ an integer