• 2 Posts
  • 45 Comments
Joined 1 year ago
Cake day: July 4th, 2023
  • Shiitake@lemmy.worldtoNo Stupid Questions@lemmy.world•What are the most mindblowing things in mathematics?
    2·
    11 months ago

    Waaaait a second.

    Does that hold for every base, where the divisor is 1 less than the base?

    Specifically hexidecimal - could it be that 5 and 3 have the same “sum digits, get divisibility” property, since 15 (=3*5) is one less than the base number 16?

    Like 2D16 is16*2+13 = 45, which is divisible by 3 and 5.

    Can I make this into a party trick?! “Give me a number in hexidecimal, and I’ll tell you if it’s divisible by 10.”

    Am thinking it’s 2 steps:

    1. Does it end with a 0, 2, 4, 6, 8, A, C, E? Yes means divisible by 2.
    2. Do the digits add up to a multiple of 5 (ok to subtract 5 liberally while adding)? Skip A and F. For B add 1; C->2, D->3, E->4. If the sum is divisible by 5, then original number is too.

    So if 1 and 2 are “yes”, it’s divisible by 10.

    E.g.

    • DEADBAE16 (=23349547010): (1) ends with E, ok. (2) 3+4+3+1+4=15, divisible by 5. Both are true so yes, divisible by 10.
    • C4744416 (=1287482010): (1) ends with 4, ok. (2) 2+4+7+4+4+4=25, ok.
    • BEEFFACE16 (=3203398350): (1) E, ok. (2) 1+4+4+2+4=15, ok.

    Is this actually true? Have I found a new party trick for myself? How would I even know if this is correct?