Pythagorean Triplets

Project Euler 139: Pythagorean tiles

Project Euler 139: Pythagorean tiles

In Project Euler There are loads of problems that end up with a number theoretic solution. Problem 139 is no exception to that.  The problem reads

Let (abc) represent the three sides of a right angle triangle with integral length sides. It is possible to place four such triangles together to form a square with length c.

For example, (3, 4, 5) triangles can be placed together to form a 5 by 5 square with a 1 by 1 hole in the middle and it can be seen that the 5 by 5 square can be tiled with twenty-five 1 by 1 squares.

However, if (5, 12, 13) triangles were used then the hole would measure 7 by 7 and these could not be used to tile the 13 by 13 square.

Given that the perimeter of the right triangle is less than one-hundred million, how many Pythagorean triangles would allow such a tiling to take place?

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Posted by Kristian in Project Euler, 6 comments
The MathBlog tools collection updated

The MathBlog tools collection updated

Just wanted to make a bit of advertisement for the tool section of the website which have been updated and new tools added.

Bjarki has been busy and developed several new tools which might come in handy for you when trying to see if a hypothesis could lead to a solution for the problem you are sitting with.

Updated tools

First of all the Prime factorization tool has been updated.  So now it gives you a little more than just the factorization. It gives you the number of distinct factors, the number of divisors and not least the value of Euler’s totient function. Yep that’s right, so head over and check it out. Continue reading →

Posted by Kristian in Other, 2 comments