== Some Equations


=== Number Theory

The equation
$a^2 + b^2 = c^2$ has infinitely many
non-proportional integer solutions.
The integer solutions of the equation
\[
  a^3 + b^3 = c^3
\]
are trivial: at least one entry is
zero and the others are "obvious"

=== Calculus

A definite integral:
\[
  \int_0^1 x^n dx = \frac{1}{n}
\]

The fundamental theorem of calculus:
\[
   \frac{d}{dx} \int_a^x f(t) dt = f(x)
\]

=== Linear algebra

A matrix:
\[
M = \left[
  \begin{array}{ c c }
	 1 & 2 \\
	 3 & 4
  \end{array} \right]
\]