#note #tag:scripta
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Theorem (Euclid). There are infinitely many prime numbers
Theorem. There are infinitley many prime number \(p \not\equiv 1 \text{ mod } 4\).
The Pythagorean formula reads \(a^2 + b^2 = c^2\).
Know this formula for the test:
\[ \int_0^1 x^n dx = \frac{1}{n+1} \]
\[ \begin{aligned} a &= p + q \\ b &= p - q \\ r &= ab \\ &= (p + q)*(p - q) \\ &= p^2 - q^2 \end{aligned} \]
Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battlefield of that war. We have come to dedicate a portion of that field, as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this.