Number Theory With Minimal Words

These Are Even!

0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0

0 0 0 0 0 0 0
0 0 0 0 0 0 0

These Are Odd!

0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0

0 0 0 0 0 0
0 0 0 0 0

Even + Even = Even!

0 0 0 0 0 0 0
0 0 0 0 0 0 0

+

A A A A
A A A A

=

0 0 0 0 0 0 0 A A A A
0 0 0 0 0 0 0 A A A A

Even + Odd = Odd!

0 0 0 0 0 0 0
0 0 0 0 0 0 0

+

A A A A
A A A A A

=

0 0 0 0 0 0 0 A A A A
0 0 0 0 0 0 0 A A A A A

Odd + Odd = Even!

0 0 0 0 0 0 0
0 0 0 0 0 0 0 0

+

  A A A A
A A A A A

=

0 0 0 0 0 0 0 0 A A A A
0 0 0 0 0 0 0 A A A A A

Multiplication!

THIS COLOR and THIS COLOR denote even parts

3 x 4 = 12!

0 0 0 0
0 0 0 0
0 0 0 0

These Are Even!

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

These Are Odd!

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0
Even X Even = Even

0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0

Even X Odd = Even

0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0

Odd X Odd = Odd

0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 



(Future additions: multiples of 'n' and why mods work)