Modulo Operation – Vortex Digit Sum is Equal to the Mod (base - 1)

4 months ago (Edited)

In this video I go over the modulo operation which returns the remainder of a division between two numbers. For example 100 mod 9 = 1 because 100/9 = 99 + 1/9, hence 1 is the remainder. I then prove that the vortex digit sum (summing the digits until a single digit is obtained) is always equal to the modulo (base - 1) of the number. For example in base 10, the remainder 67 mod 9 = 4 v= 6 + 7 = 13 v= 1 + 3 = 4. This works for any base number system!

#math #vortexmath #modulararithmetic #algebra #education

7 Modulo Operation Proof.png

Timestamps

Determining Remainders with the Modulo Operation – 0:00
a modulo n or a mod n is the remainder of a / n – 0:28
Vortex sum, repeating digits of division, and modulo operations appear to be equal – 0:47
Note 1: Vortex sum of 9 gives a mod of 0 – 1:41
Note 2: Typical convention is 12 = 3 (mod 9) but I will use "v=" notation – 2:15
Proof: The Vortex Digit Sum = Mod (base - 1) – 3:26
- Base 10 proof: Let a, b, c between integers between 0 and 9 – 5:15
- Expanding the number abc into multiples of 9 obtains the first digit sum, then repeat the process until we obtain the vortex sum – 6:06
Summarizing the proof for mod 9 – 9:30
Generalization proof for any other base system – 10:25
- Remainder is always the vortex digit sum: abc mod (base - 1 = p) = vortex digit sum – 12:35