Square Factorization Using Addition and Subtraction
Sven Gelbhaar
Salutations,
Computers are orders of magnitude faster at addition and subtraction than they
are at multiplying and dividing. Therefore, I was motivated to come up with a
method of deriving perfect squares using only addition and subtraction. It took
enormous effort, working under the threat that there might not be a viable
method of doing this, but humanity persevered. This could help to eliminate
potential prime numbers in a cryptographic setting, or it could be construed as
a sign of intelligent design; this being just one of god(s)’ Easter Eggs.
Either way, the +3 at the end should be referred to as the Gelbhaar Constant.
Thanks in advance.
(|x|^2) = (x – 1) + ((x – 1)^2 – (x – 1)) + ((x – 1)^2 – (x – 1) – ((x – 2)^2 –
(x – 2)) + 3
I realize that this could be reduced further, but I’ll leave that as an exercise
for the reader.
11 May 2011
Sven Gelbhaar