Other diophantine equations solved thanks to modularity theorem
40087
Using Modularity Theorem and Ribet's Theorem to disprove existence of rational solutions
94917
Prove that for every prime $p$, there exists a solution to $(x^2-2)(x^2-6)(x^2-3) \equiv 0 \mod(p)$
51445
Number Theory: Find all solutions of $\phi(n)=16$ and $\phi(n)=24$
21530
How many solutions of $\mod 63$ : $x^2=1 \pmod7 $ and $x^3=1\pmod 9$
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.
56803
Finding solutions to congruence equations
156966
Prove that if $b = dk$ where $gcd(m, a) = d$, there are $d$ solutions to $ax \equiv b \mod m$
136856
Diophantine equation with a prime number
135465
Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$
21108
Perfect squares and modularly congruency in mod 5
42754
Modular arithmetic: division, fractions, solving linear congruences
2027
How can I solve the folowing Diophantine equation with two unknowns?
109490
Modular arithmetic problem (mod $13$)
52530
There exists a prime congruent to $m$ mod $p$
127945
Number of solutions to the congruence $x^q \equiv 1 \mod p$.
115244
Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
78638
Find out all solutions of the congruence $x^2 \equiv29 \mod 5$.