Recent content by Imaginer1

I've thought about it, but haven't. Don't assume, however, that implies my knowledge on number theory doesn't stack up- actually, I'm currently working with the Mertens function growth rate, but that's a bit beyond the point.

Yes. Those seem exceedingly entertaining. I SHALL BEGIN.

I am a freshman in High school, however I've been working quite a lot in the field of number theory for quite some time. However, I've been beginning to feel slightly bad that I haven't actually proven anything. It's not like I want to make a brand new theorem, no; but I would like to start to...

I've noticed lots of interesting properties of the patterns of numbers in the Fibbonacci sequence that can be expressed as the sum of two squares. In fact, it's what got me into number theory in the first place. There seem to be no two adjacent entries that are not the sum of two squares- and it...

There's an interesting sequence that creates tons of large numbers before reaching zero: -Take an arbitrary number N and express it in base-2 hereditary notation (that all coefficients are less than or equal to 2, eg 35= 25+21+1 however the exponent 5 is greater than 2, we will express that...

Even though this is my first post on Physics Forums and this was done a year ago, I'm going to tell everyone you've made it way too complicated. I'm a pretty new mathematician, and I feel this isn't in the spirit of a proof, but it still works. Take the case n^2. if n==0 (mod 4), n^2 will...