If $a_{1}=1$ and for n>1, $a_{n}=a_{n-1}+\frac{1}{a_{n-1}}$ , then $a_{246}$ lies between two integers, what are they?
139207
How to find range $a_{75}$ of the term of the series $a_n=a_{n-1}+ {1 \over {a_{n-1}}} $
81822
How many integers between $1$ and $10^4$ contain exactly one $8$ and one $9$?
101491
If $\frac{a}{|z_2-z_3|}=\frac{b}{|z_3-z_1|}=\frac{c}{|z_1-z_2|}$, then why is $\frac{a^2}{z_2-z_3}+\frac{b^2}{z_3-z_1}+\frac{c^2}{z_1-z_2}=0$?
126354
Find all positive integers $a, b, c$ such that $1/a + 1/b + 1/c = 4/3999$
86413
Show that $\frac{(m+n-1)!}{m!n!}$ is an integer where m and n are positive integers and gcd(m,n)=1
13317
show that $a^{12} \equiv 1 \mod 32760$ for each $a \in \mathbb{Z}$ such that $\text{gcd}(a, 32760) = 1$
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
146169
Integer solutions to $\frac{1}{a} + \frac{1}{b} = \frac{1}{12}$.
56574
For any integer $a,b$ let $N_{a,b}$ denote the number of positive integer $x<1000$ satisfying $x= a( mod\;27)$ and $x=b(mod\;37)$. Then
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
67528
"If $1/a + 1/b = 1 /c$ where $a, b, c$ are positive integers with no common factor, $(a + b)$ is the square of an integer"
97684
Show $\frac{(2n)!}{n!\cdot 2^n}$ is an integer for $n$ greater than or equal to $0$
118574
prove that $24 \mid a(a^2-1)$
126471
At least one prime between $\sqrt{n}$ and $n$?
122916
Does $[0.9999....]=1$?
36083
If $k > 1$, then $\frac1{(k - 1)^2}-\frac1{(k + 1)^2}=\frac{4k}{(k^2 - 1)^2}$, hence simplify $\sum\limits_{k = 2}^n\frac k{(k^2 - 1)^2}$
41141
Proving that $\frac{\phi^{400}+1}{\phi^{200}}$ is an integer.