Merge project euler

projecteuler/.gitignore

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+*.aux
+*.fdb_latexmk
+*.fls
+*.log
+*.out
+*.pdf
+*.synctex.gz

projecteuler/problem_1.cpp

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+#include <iostream>
+
+int problem1_s(unsigned int n, unsigned int d) {
+  unsigned int m = (n - 1) / d;
+  return d * m * (m + 1) / 2;
+}
+
+int problem1(unsigned int n) {
+  return problem1_s(n, 3) + problem1_s(n, 5) - problem1_s(n, 15);
+}
+
+int main() {
+  std::cout << problem1(1000) << std::endl;
+  return 0;
+}

projecteuler/problem_1.tex

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+\documentclass{article}
+\usepackage{mathtools}
+\usepackage{amsfonts}
+\usepackage{amsmath}
+\DeclarePairedDelimiter\ceil{\lceil}{\rceil}
+\DeclarePairedDelimiter\floor{\lfloor}{\rfloor}
+
+\begin{document}
+  \section{Multiples of 3 and 5}
+  Problem 1
+
+  If we list all the natural numbers below 10 that are multiples of 3 or 5,
+  we get 3, 5, 6 and 9. The sum of these multiples is 23.
+
+  Find the sum of all the multiples of 3 or 5 below 1000.
+
+  \begin{equation*}
+    \begin{split}
+      m &= \floor*{\frac{n-1}{d}} \\
+      s(n,d)
+      &= \sum\limits_{i=1}^{m} di \\
+      &= d\sum\limits_{i=1}^{m} i \\
+      &= d\frac{m(m + 1)}{2}
+    \end{split}
+  \end{equation*}
+  \begin{equation*}
+    \begin{split}
+      f(n) &= s(n, 3) + s(n, 5) - s(n, 15) \\
+      f(1000)
+      &= s(1000, 3) + s(1000, 5) - s(1000, 15) \\
+      &= 3\frac{333\cdot334}{2}
+      + 5\frac{199\cdot200}{2}
+      - 15\frac{66\cdot67}{2} \\
+      &= 166833 + 99500 - 33165 \\
+      &= 233168
+    \end{split}
+  \end{equation*}
+\end{document}