how many integers $n$ have the property that there exist positive integers $a,b,c$ such that $a^n+b^ n=c^n$?
4140
Fermat's Last Theorem with negative exponent
59535
Prove that there exists such a set of $n$ positive integers
63651
If $(a,b)=1$ then there exist positive integers $x$ and $y$ s.t $ax+by=1$.
71012
If $a, b$ are positive integers such that $a|b^2, b^2|a^3,....$ then $a=b$.
64654
Suppose $a, b$ and $n$ are positive integers. Prove that $a^n$ divides $b^n$ if and only if $a$ divides $b$.
89175
Proof of $(a+b)^{n+1}$
49372
$x+1/x$ an integer implies $x^n+1/x^n$ an integer
91113
$ \exists a, b \in \mathbb{Z} $ such that $ a^2 + b^2 = 5^k $
31436
Show that for all $a\in\mathbb{N}$, there exists $b\in\mathbb{N}$ and square-free integer $c$ such that $\sqrt{a}=b\sqrt{c}$.
6970
If $abc=1$ and $a,b,c$ are positive real numbers, prove that ${1 \over a+b+1} + {1 \over b+c+1} + {1 \over c+a+1} \le 1$.
63931
When $ab/(a+b)$ is an integer, where $a,b$ are positive integers.
20003
Prove for positive integers a,b,c and d (where b does not equal d), if gcd(a,b) = gcd(c,d) = 1, then a/b + c/d is not an integer
101519
What is the condition for example $(number^c)^b=number^{cb}$ to be true?
134121
Determining all the positive integers $n$ such that $n^4+n^3+n^2+n+1$ is a perfect square.
60284
Infinitely many positive integers $n$ such that $\phi(n) = \frac{n}{4}$?
38882
If $n$ is a positive integer such that $n^3 − n − 6 = 0$, then, for every positive integer $m$ with $m \not = n$, $m^3 − m − 6 \not = 0$.
114404
For which positive integer values of $n$ does $a|mn-b?$