Where numbers rule

One of my favorite expressions from my research is simply a sum of seven squares to get a square:

34967² + 752² + 1128² + 1880² + 2632² + 4136² + 4888² = 35721²

Where am using my BQD Iterator, and have put up repeatedly and like to use to remind that numbers DO rule. And with me? Number theory should show number theory results, with integers.

Am NOT a mathematician. Am a mathematical discoverer.

For a bit thought maybe mathematicians couldn't do such sums, as was just doing web searches but finally with one, as I do keep searching, found a paper which stated was summing seven squares to a square.

Another example I like where have not seen anything like it elsewhere, which does not mean is not out there:

(46² + 48² + 72²)(172² + 258² + 430² + 602² + 1762²) = 

            615² + 3075² + 14145² + 15990²  + 188497²   =  77⁴*2¹⁰

Which is still using my BQD Iterator as that thing is really useful, and really cool.

For me number theory should have such things. I like looking at them, and understanding the relationships between integers that make such possible, and easy to generate.

Numbers DO rule. And should rule, number theory.


James Harris