Vortex Math is Based on the Modulo Multiplication Identity

In this video I show that the previous result of "multiplying a number and its vortex sum yields the same vortex sum" can be written in its equivalent modulo multiplication identity. Since we have already established that the vortex sum of an integer (summing the digits until we get a single digit) is the same as the modulo of that number with the modulus being the base - 1, we can rewrite the vortex sums using the modulo operations. In general, if we have integers A, B, and C, then we have the identity AB mod C = [A·(B mod C)] mod C. Furthermore we can apply this same identity with the integers inside the bracket to also get it equal to [( A mod C)(B mod C)] mod C and [(A mod C)·B] mod C. Pretty epic stuff!

#math #vortexmath #modulararithmetic #numbertheory #education

10 Modulo Multiplication Identity.png

Timestamps

Vortex math multiplication as an equivalent modulo identity – 0:00
25 * 4 = 100 v= 1 or 25 v= 7 * 4 = 28 v= 1 – 0:38
(4 * 25) mod 9 = [4 * (25 mod 9)] mod 9 = 1 – 1:59
Generalize modulo operation to any integer multiple or modulus: (AB mod C = [A(B mod C)] mod C = [(A mod C)(B mod C)] mod C = [(A mod C)B] mod C – 3:00
Example: A = 11, B = 22, C = 7 – 4:44
Reason is because modulo operation gives integers, which can just apply the same identity over again – 5:51
– Modulo of a multiplication of integers is the same as the modulo of the multiplication of either or both modulo of the integers – 6:54