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I graduated in mathematics sometime in a past, now I work as a software engineer.

Some interesting topics:

$x^j+x^k+2$ is irreducible over $\mathbb{Q} \iff \nu_2(j) \neq \nu_2(k)$

$x^m+y^n$ is irreducible over $\mathbb{Q} \iff \gcd(m,n)=2^k$

If polynomials $P(x)=Q(y)$ for infinitely many integers $x,y$, then $P(x)=Q(R(x))$

$c_0+c_1x+\dots+c_nx^n=a_0+a_1\binom{x}{1}+\dots+a_n\binom{x}{n}$ with $a_i = i!\sum_{k=i}^{n}{k\brace i}c_k$

If $f(x)=a_0+a_1x+\dots+a_nx^n$ then $\gcd(f(0),f(1),\dots)$ divides $\gcd(a_0,\dots,a_n)\cdot n!$

$\frac{7}{8} \zeta(3)=\frac{1}{p(0)-\frac{1^6}{p(1)-\frac{2^6}{p(2)-\ddots}}}$ where $p(n)=6n^3+9n^2+5n+1$