Is there only one pair of unequal rational numbers with $n^m = m^n$?
5595
$x^y = y^x$ for integers $x$ and $y$
12701
Perfect set without rationals
33138
Is Rational number under multiplication group?
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
146312
Is the set of roots with respect to their values and multiplicies unique for each $g(x)$ in $a_n x^n + g(x)$?
22391
Is the set of all pairs of real numbers uncountable?
2884
$m,n>1$ are relatively prime integers , then are there at-least four idempotent (w.r.t. multiplication) elements in $\mathbb Z_{mn}$ ?
79638
Number of solns of $x^6+x=a$ in $\mathbb{F}_{2^m}$, where $m\geq 3$ is odd is same as number of solns of $x^2+ax+1=0$
86893
Show that it is impossible to list the rational numbers in increasing order
8884
Find all natural numbers $n$ and $m$ for which $n^m=(n-1)!+1$
52012
Is there exist a homemoorphism between either pair of $(0,1),(0,1],[0,1]$
112575
Finding integer solutions of $m^2-n^5 = m - n$
148585
Show that, for any $\epsilon>0$, there exist two rationals such that $q < x < q'$ and $|q-q'|<\epsilon$
31698
$f(m^2 + f(n)) = f(m)^2 + n$ for all natural numbers
18018
Proving that $4 \mid m - n$ is an equivalence relation on $\mathbb{Z}$
158563
If $m^4+4^n$ is prime, then $m=n=1$ or $m$ is odd and $n$ even
151544
Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$