# I Love Number Theory

## Prime Numbers

Anyone familiar enough to speak "math" knows of Fourier Series, which can be used to approximate ANY function [even the STEP function, which astonished me]. I wonder if, instead of using all the periods in the sine functions composing a Fourier series, what would happen if you...
freeed
66-70, M
1 Response Feb 26, 2010

## Favorite Number Theory Fact

Here's my favorite number theory fact I've come across so far - but that's probably just because it's the one I've proved most recently. 1^3 + 2^3 + 3^3 + ... + n^3 = (1 + 2 + 3 + ... + n)^2 In English, the sum of the first n consecutive cubes is always equal to the square...
Atrytone
22-25, F
6 Responses Feb 24, 2010

## Integer Squares

Maybe not as interesting as other facts, but I recently tripped over this "interesting property": Every prime number that leaves ONE as a remainder when divided by four can be expressed as the sum of two intergers squared, e.g. 97 = 9^2 + 4^2 [97/4 = 24 + 1] Prime numbers of...
freeed
66-70, M
4 Responses Apr 16, 2010