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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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