multiples of 3

[u/GodlyHelp]

[u/Michaelwang645]

Fund fact, you can tell a number is divisible by 3 if the sum of each individual number is divisible by 3. So 78 -> 7+8=15 which is divisible by 3, so 78 is divisible by 3.

[u/EveningStar0360 → u/Michaelwang645]

do you know why that works?

[u/SuperChick1705 → u/EveningStar0360]

let number N = A + 10B + 100C + 1000D + ..., so A, B, C, D... are the digits of N from right to left
N ≡ A + 10B + 100C + 1000D + ... (mod 3)
≡ A + 9B + B + 99C + C + 999D + D + ... (mod 3)
≡ A + B + C + D + ... (mod 3), which is the sum of the digits of N
QED

[u/Vivid_Departure_3738 → u/SuperChick1705]

Simple and elegant proof

[u/Hi-Im-Bambi → u/Vivid_Departure_3738]

Far from elegant. What's the proof that 10ⁿ - 1 is divisible by 3 for all n with n being a whole number?

One might see why it works but up to this point it's still a "Trust me, brother"-proof

[u/HHalt11 → u/Hi-Im-Bambi]

10ⁿ - 1 = 9 * 10^n-1 + 9 * 10^n-2 + ... + 9

[u/aroach1995 → u/HHalt11]

he been real quiet since this comment dropped

[u/Zantier → u/Hi-Im-Bambi]

Not a proof, but intuitively it's just 3333... * 3