uniqueness of solutions of $ax=b$ and $ya=b$ in a semigroup .
56650
Prove that $(G, \circ)$ is a group if $a\circ x = b$ and $x\circ a = b$ have unique solutions
29096
Non-uniqueness of solutions of the heat equation
109512
Let f,g be bilinear forms on a finite dimensional vector space. Show that there exist unique linear operators
111406
Proving that a definition of e is unique
42516
If every $x\in X$ is uniquely $x=y+z$ then $\|z\|+\|y\|\leq C\|x\|$
132239
Why is the solution single-valued?
46028
Show that the solution for the Diophantine equation $x^2 - y^2 = N$ is unique if and only if $|N|$ or $\frac{|N|}{4}$, respectively, is $1$ or prime.
5226
Prove that a finite semigroup G with identity is a group if and only if G contains only one idempotent
32071
General solution of linear equation = particular + general homogeneous solution
121765
Semigroups and solutions of equation
94037
Solving the matrix equation $AP=PB$, where $A$ and $B$ are similar
14773
Finding distinct solutions for the equation
34099
Proving that the empty set is unique
70606
Show that the LU decomposition of matrices of the form $\left[\begin{smallmatrix}0& x\\0 & y\end{smallmatrix}\right]$ is not unique
158724
Show that $B$ is diagonalizable if If $AB=BA$ and $A$ has distinct real eigenvalues
142519
Uniqueness and Existence problem
7536
Is there an idempotent element in a finite semigroup?