Let $x$ and $y$ be integers such that $x ≡ 3$ (mod $9$) and y ≡$ 4$ (mod $9$). Is it possible that $ 20x + 3y^3 ≡ 6$ (mod $9$)
11500
Divisibility by 7 rule, and Congruence Arithmetic Laws
127183
Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$
23866
Do there exist an infinite number of integer-solutions $(x,y,z)$ of $x^x\cdot y^y=z^z$ where $1\lt x\le y$?
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
53325
Are there integer solutions to $9^x - 8^y = 1$?
19164
On the GCD of a Pair of Fermat Numbers
38882
If $n$ is a positive integer such that $n^3 − n − 6 = 0$, then, for every positive integer $m$ with $m \not = n$, $m^3 − m − 6 \not = 0$.
80058
Three variable, third degree Diophantine equation
46606
Can an integer of the form $4n+3$ written as a sum of two squares?
51221
Is $x^3-9$ irreducible over the integers mod 31?
59442
Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
75957
Prove $x^3+3y^3+9z^3-9xyz=1$ has infinity integers solutions!
105442
Show that any prime divisor of $x^4+x^3+x^2+x+1$, with $x\in\mathbb{N}$, is $5$ or $1$ mod $5$
87267
Conjecture similar to Fermat's Theorem.
47232
Prove $\forall a,b,c \in \mathbb Z$, if $ab+ac\equiv 3\pmod 6$ then $b \not\equiv c \pmod 6$ by contraposition
94700
Integer solutions for $x^3+2=y^2$?
127816
Number theory proof mod p