Show that $8 \mid (a^2-b^2)$ for $a$ and $b$ both odd
63774
If a and b are odd integers, then $8\mid (a^2-b^2)$
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
87522
If $ a + b + c \mid a^2 + b^2 + c^2$ then $ a + b + c \mid a^n + b^n + c^n$ for infinitely many $n$
40030
FA that accepts odd number of $b$ and even number of $a$
19525
Showing field extension $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5})/\mathbb{Q}$ degree 8
130104
Show $4x^2+6x+3$ is a unit in $\mathbb{Z}_8[x]$ (inverting unit + nilpotent)
12862
Prove that two distinct numbers of the form $a^{2^{n}} + 1$ and $a^{2^{m}} + 1$ are relatively prime if $a$ is even and have $\gcd=2$ if $a$ is odd
128060
Proof that the relation $5 \mid (a + 4b)$ is symmetric and transitive
10236
Show that $a^n \mid b^n$ implies $a \mid b$
24466
Prove that if $[F(\alpha):F]$ is odd then $F(\alpha)=F(\alpha^2)$
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$
52930
Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$
140294
prove that $n >2$ and $n$ is a prime then $n$ is odd
121177
Prove that $\frac{(2a+b+c)^2}{2a^2+(b+c)^2}+\frac{(2b+c+a)^2}{2b^2+(c+a)^2}+\frac{(2c+a+b)^2}{2c^2+(a+b)^2} \le 8$
7491
How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?
85272
$3x + 1$ is even iff $5x-2$ is odd
94326
a square in a finite field of odd order