A Pythagorean triplet is a set of three natural numbers, $a, b, c$, for which, $a^2 + b^2 = c2$ For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2. There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.
Project Euler - Problem 9. This problem has been solved by 75913 people, ( problem 1 by 159750 people ).
When you have solved a problem you get access to the answer book. It then becomes clear what a difference it makes if you are somewhat literate in a tool like Mathematica. I have solved most problems so far, if not all. with one line of functional Mathematica code while the model answer is a three or four page pdf full of procedural code. - For a while I had the feeling I was cheating by using Mathematica, but the goal is clear. Solve. no matter what. I am not sure but I think Euler is mainly geared for computer geeks, although the problems so far could have been solved by intelligent programming alone, knowledge of mathematics makes a difference. Take this problem for example.
2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
Project Euler - Problem 5.
Solved this one without using my computer, thus simple. Because I have done an introductory course in Number Theory of course. Maybe it is not so simple otherwise, I don't think so actually.
If you are ever enjoying leisure time on Sudoku's, Euler is worth considering. More fun!
Watched the movie Source code yesterday. Liked it so much that I will give Proof ( Jake Gyllenhaal has a part in it ) a second chance. Proof is not an action movie, it is more in the line of A Beautiful Mind. An attempt to answer "Where does genius end before it turns into undeniable insanity?"