Find all possible values $a,b\in [0,10^9]$ such that $a+b=ab$
35066
Nature and number of solutions to $xy=x+y$
76925
Algebraic proof that if $a>0$ then $1+a^9 \leq \frac{1}{a}+a^{10} $
48404
If $a$ and $b$ are integers such that $9$ divides $a^2 + ab + b^2$ then $3$ divides both $a$ and $b$.
140167
Proving $A+A'B=A+B$ without truth tables
9149
Any $B \subset \{10,11,...,99\}$, with $|B| =10$ has two subsets such that $\sum_{a \in B_1} a = \sum_{b \in B_2} b$
86841
Find a matrix $B$ such that $B^3 = A$
151012
Find the value of $\lfloor x+y \rfloor$ where $x \in \mathbb{R}$, $y \in \mathbb{Z}$
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
70619
Supposed $a,b \in \mathbb{Z}$. If $ab$ is odd, then $a^{2} + b^{2}$ is even.
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
103545
Prove "casting out nines" of an integer is equivalent to that integer modulo 9
117380
Divisibility Rule for 9
112867
Find all digits $a,b$ such that the number $\overline{aabb}$ is a perfect square
91451
find all positive integer $m,n$
143501
Find all $n\in\mathbb N^+$ such that the sum of the digits of $5^n$ is equal to $2^n$.
112368
Is there a rule for $\sqrt{a+b}$?
69874
Are there any integer solutions to $a^3=b^2$?