Proof that there must exist infinitely many solutions to a homogeneous system of equations when more unknowns than equations
36998
In $Ax=b$. If $A$ is not invertible there are no solutions or infinity. How to determine what the case is?
32071
General solution of linear equation = particular + general homogeneous solution
112390
Solutions of $x^2 \equiv 1 \pmod N$
20034
Does $a^2+b^2=1$ have infinitely many solutions for $a,b\in\mathbb{Q}$?
156468
Solutions to $a+b+c=12$, $a, b, c \in \mathbb{N}_0$
77763
Proof that the equation $x^2 - 3y^2 = 1$ has infinite solutions for $x$ and $y$ being integers
74452
On a uniqueness proof for solutions of $\ a + x = b\,$ in a group
103197
number of distinct solution of Integral equation
95494
Number of solutions of an arithmetic function's equation
55966
Multiple solutions for a particle in an infinite potential well
128107
find all $ a \in \mathbb N $ such that $2^a − 1 \equiv 0 \pmod 3$ and $ 4x^2 + 1 \equiv 0 \pmod {\frac{2^a -1}{3}}$ has a solution
40087
Using Modularity Theorem and Ribet's Theorem to disprove existence of rational solutions
150674
Uniqueness in existence of a bilinear form
65000
prove that $x^2 + y^2 = z^4$ has infinitely many solutions with $(x,y,z)=1$
27540
A polynomial can not have infinite number of constant values
91003
Prove that equation has exactly 2 solutions
29078
find all the values of a and b so that the system has a) no solution b) 1 solution c) exactly 3 solutions and 4) infinitely many solutions