Does there exist an integer $x$ satisfying the following congruence:
107990
Does there exist an integer $x$ satisfying the following congruences?
63129
Infinite number of $k$ satisfying $p_{k+1} - p_{k} > 2$?
115435
Induction: prove using congruences
152172
Does there exist a positive irrational number $\alpha $, such that for any positive integer $n$ the number $\lfloor n\alpha \rfloor$ is not a prime?
94917
Prove that for every prime $p$, there exists a solution to $(x^2-2)(x^2-6)(x^2-3) \equiv 0 \mod(p)$
33735
The square of an integer is congruent to 0 or 1 mod 4
53231
A slightly stronger version of the Goldbach conjecture?
156940
There does not exist a polynomial $p(x)$ with integer coefficients which gives a prime number $\forall x\in \mathbb{Z}$
81267
A simple doubt in number theory problem.
29204
$a\equiv\bar a\!\pmod{\!kn}\Rightarrow a\equiv\bar a\!\pmod{\! n};\ $ $(a\bmod kn)\bmod n=a\bmod n.\ $ Congruences persist mod factors of the modulus
53525
Infiniteness of non-twin primes.
123441
Quadratic congruences problem $(x^2-a)(x^2-b)(x^2-ab)$ ≡ 0 (mod p)
131941
Solve quadratic congruences.
513
If n is an odd integer, show there exists a positive integer k such that 2^k mod n = 1.
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
114185
Existence of $x$ such that $2^x =a,3^x=b,5^x=c$ for some integers $a,b,c$
17786
Existence of Consecutive Quadratic residues