I successfully compiled my program. Now how do I run it?

Question

I want to solve Project Euler 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.

Here's my code:

\documentclass[10pt,a4paper]{article}
\usepackage{hyperref}
\newcommand*\rfrac[2]{{}^{#1}\!/_{#2}}
\title{Solution to Project Euler Problem 1}
\author{Aadit M Shah}
\begin{document}
\maketitle
We want to find the sum of all the multiples of 3 or 5 below 1000. We can use the formula of the $n^{th}$ triangular number\footnote{\url{http://en.wikipedia.org/wiki/Triangular_number}} to calculate the sum of all the multiples of a number $m$ below 1000. The formula of the $n^{th}$ triangular number is:

\begin{equation}
T_n = \sum_{k = 1}^n k = 1 + 2 + 3 + \ldots + n = \frac{n (n + 1)}{2}
\end{equation}

If the last multiple of $m$ below 1000 is $x$ then $n = \rfrac{x}{m}$. The sum of all the multiples of $m$ below 1000 is therefore:

\begin{equation}
m \times T_{\frac{x}{m}} = m \times \sum_{k = 1}^{\frac{x}{m}} k = \frac{x (\frac{x}{m} + 1)}{2}
\end{equation}

Thus the sum of all the multiples of 3 or 5 below 1000 is equal to:

\begin{equation}
3 \times T_{\frac{999}{3}} + 5 \times T_{\frac{995}{5}} - 15 \times T_{\frac{990}{15}} = \frac{999 \times 334 + 995 \times 200 - 990 \times 67}{2}
\end{equation}
\end{document}

I compiled it successfully using pdflatex:

$ pdflatex Problem1.tex
This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2014/Arch Linux) (preloaded format=pdflatex)
.
.
.
Output written on Problem1.pdf (1 page, 106212 bytes).
Transcript written on Problem1.log.

It generated the following output PDF file along with a bunch of other files with scary extensions:

How do I run this PDF file so that it computes the solution? I know the solution to the problem but I want to know how to execute the PDF file to compute the solution.

The reason why I prefer LaTeX over other programming languages is because it supports literate programming, an approach to programming introduced by Donald Knuth, the creator of TeX and one of the greatest computer scientists of all time.

Edit: It would also be nice to be able to print the computed solution either on the screen or on paper. Computing the solution without printing it is useful for heating the room but it is so hot already with the onset of summer and global warming. In addition, printing the solution would teach me how to write a hello world program in LaTeX.

Answer 1

So, today seems to be a safe day to tackle this problem...

---

The OP does not seem to be quite so PDF-savvy. However, he obviously is quite a literate LaTeX guy. Which means, he also must be knowing TeX very well, given he is so much of a Donald Knuth admirer...

So much for the preliminaries. Now for the real meat.

First, to quote the official PDF-1.7 specification document:

PDF is not a programming language, and a PDF file is not a program.
                                                                                                            (p. 92, Section 7.10.1)

However, the pre-decessor of the PDF format, PostScript, IS a Turing-complete programming language... Turing-complete, just as TeX is, the creation of Donald Knuth, one of the greatest computer scientists of all time.

PostScript files, on the other hand, ARE programs, and can easily be executed by PostScript printers (though this execution time cannot reliably be determined in advance).

Hence, and second, the OP should be able to find a way to convert his hi-level LaTeX code to low-level TeX code. That code needs to emit a PostScript program, which in turn can be executed by a PostScript printer. Writing that TeX code should be trivial for somebody like the OP, once he is given the PostScript code that should be the result of his TeX code.

I myself am not so well-versed with the TeX aspect of that problem solving procedure. However, I can help with the PostScript.

The PostScript which the OP's TeX code should produce goes like this (there are for sure more optimized versions possible -- this is only a first, quick'n'dirty shot at it):

%!PS

% define variables
/n1 999 def
/t1 334 def
/n2 995 def
/t2 200 def
/n3 990 def
/s1  67 def
/t3   2 def

% run the computational code
n1 t1 mul
n2 t2 mul
n3 s1 mul
sub
add
t3    div

% print result on printer, not on <stdout>
/Helvetica findfont
24 scalefont
setfont
30 500 moveto
(Result for 'Project Euler Problem No. 1' :) show 
/Helvetica-Bold findfont
48 scalefont
setfont
80 400 moveto
(                   ) cvs show 
showpage

Send this PostScript code to a PostScript printer, and it will compute and print the solution.

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Update

To answer one of the comments: If you replace the last section of PostScript code starting with /Helvetica findfont with a simple print statement, it will not do what you might imagine.

print does not cause the printer to output paper. Instead it asks the PostScript interpreter to write the topmost item on the stack (which must be a (string)!) to the standard output channel. (If the topmost item on the stack is not of type (string), it will trigger a typecheck PostScript error.)

So sending a modified PostScript file (where print has replaced the last section of my PS code) to the printer will not work (unless that printer supports the interactive executive PostScript mode -- which is not a standard part of the PostScript language). It will work however if you feed that file to Ghostscript in a terminal or cmd.exe window.