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== Some Equations


=== Number Theory

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

=== Calculus

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

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

=== Linear algebra

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

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