Why 15 and 290 are cool (making numbers out of sums of squares)

Given a particular recipe for making numbers out of sums of squares, such as x^2 + y^2 or 3x^2 + 5y^2 + 7z^2, when can the recipe make all positive integers? And if you have a recipe that you have successfully tested on all small numbers, can you be confident it will work for all numbers? Some of these questions have recently (last 20 years) been answered by John Conway, Manjul Bhargava, and others. But what do 15 and 290 have to do with it? Well, watch the videos:


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s