Math!

Yes, Math Factorial (old old joke I know).

I couldn’t leave out my favorite subject from this site.  It’s closely followed by basically all of the sciences.  How much will end up on the site is unknown.

Throughout college, I tried to pick research in topics that are easily explained to non-math majors.

Here are some research projects I worked on (almost entirely alone):

ABC “Rad” Triples: (This was originally posted with TeX script.  I’ll post an image or pdf eventually.)

Rad(n) is the product of all of the Prime factors of n.  Rad(15) = 15 because 3 and 5 are the prime factors and their product is 15.  Rad(8) = 2 as 2 is the only prime factor of 16.  Rad(9) = 3.

We want to find 3 whole numbers > 0 that don’t share ANY Prime factors with each other.  Also the two lesser numbers must add to the third.  Finally the rad of the product must be less than the largest.

Example: (1, 8, 9).  No prime factors shared.   1 + 8 = 9 .  rad(1*8*9) < 9.

(3, 125, 128).  No prime factos shared.  3 + 125 = 128.  rad(3*125*128) < 128.

There are other examples where all three numbers less than a hundred.  Can you find them?

A Proof That There are infinitely many ABC-Triples of the form (sx^n, ty^n – sx^m, ty^n) for any pairwise relatively prime quadruple of positive integers (s, x, t, y). from puremathematics

Not a lot of points, but it was 100% upvoted.

Random ({}, *) With Closure:

Given n, a whole number > 0, (Set of all magic squares n x n, position-wise addition)

(fibonacci — yes lowercase, term-wise addition)

a = 1, 4, 5, 9, 14 …
b = 5, 3, 8, 11, 19 …
a + b = 6, 7, 13, 20, 33 …

(All lines but excluding x = k for every constant k, polynomial addition)

(All geometric sequences, term-wise multiplication)

a1 = 2, 10, 50, 250 …
a2 = 16, 24, 36, 54 …
a1 * a2 = 32, 240, 1800 …