How to show that $x^2\equiv 2 \pmod {11}$ has no solution.
68635
When is $2$ a quadratic residue mod $p$?
39346
Let $R= \mathbb{Q}[x^2 ,x^3 ]$, the set of all polynomials over $\mathbb{Q}$ with no $x$ term. Show that the $\gcd$ of $x^5$ and $x^6$ does not exist
23301
There does not exist any integer $m$ such that $3n^2+3n+7=m^3$
41890
How to get all solutions of $x^2 \equiv$ $a$ mod $p$?
127945
Number of solutions to the congruence $x^q \equiv 1 \mod p$.
34192
Solve $x^{5} \equiv 2$ mod $221\ $ [Taking modular $k$'th roots if unique]
61987
$x^2+1=0$ in $\mathbb{Z}_7$
32391
Show that $x^2+x+4$ is irreducible over $\mathbb Z_{11}$.
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
18093
Find $x$ such that $\sum_{k=1}^{2014} k^k \equiv x \pmod {10}$
124241
Finding all integers $k \geq 2$ such that $k^2 \equiv 5k \pmod{15}$. What is going on here?
84379
Prove that there is no integer a for which $a^2 - 3a - 19$ is divisible by 289
32985
Prove that there does not exist integer solutions for the diophantine equation $x^5 - y^2 = 4$.
50182
Prove the Mordell's equation $x^2+41=y^3$ has no integer solutions
107448
proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$
53139
How to demonstrate that there is no all-prime generating polynomial with rational cofficents?
18767
How do you find the modular inverse of $5\pmod{\!11}$