Why if a system $AX=Y$ has solutions in a field F then it has solution in a subfield F_1?
22192
System of linear equations having a real solution has also a rational solution.
74452
On a uniqueness proof for solutions of $\ a + x = b\,$ in a group
156966
Prove that if $b = dk$ where $gcd(m, a) = d$, there are $d$ solutions to $ax \equiv b \mod m$
19511
Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?
69839
Prove that a system of linear equations, will have infinitely many solutions whenever there is a specific value.
48652
Solve the functional equation $2f(x)=f(ax)$ for some $a$.
79925
Infinitely many values of $x$ that satisfy the equations
133101
Number of solutions of $P(x)=e^{ax}$ if $P$ is a polynomial
148192
In a field that is the direct product of two fields, why isn't it a field?
104609
For which $a$ does the equation $f(z) = f(az) $ has a non constant solution $f$
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
83009
Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
20568
Does the following have a solution for f(x,y)?
15312
Show that $R \cap R^{−1}$ is an equivalence relation on $X$?
125647
Solutions to the matrix equation $\mathbf{AB-BA=I}$ over general fields
151732
Number of solutions of polynomials in a field
71203
Proving that two systems of linear equations are equivalent if they have the same solutions