• 2 Posts
  • 11 Comments
Joined 1 year ago
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Cake day: June 14th, 2023

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  • Oh, that’s just the tip of the proverbial iceberg. I’ve got plans to incorporate a plaque that can be hung on a wall afterwards, that will use elements of both her grandpa, great uncle, and this uncle, heh. I’ve got my part figured out, just need to finish the other two…and I think I just got my dad’s figured out. He was known for growing russian olives, and there’s only a few branches left…I could carve a heart in a cross section, and place one of my claws in side of it…That’s what I’ll do…Now just one more…For our great uncle…We’ll be heading to his farm to find something next week. 🤞





  • I did find that it can be done arbitrarily. Mind is definitely not into writing about it, though, but here’s the gp code I wrote to look it over.

    /*
        There may exist a 0<=t<s such that
        s divides both x and (x+(x%d)*(t*d-1))/d.
    
    
        To show this for solving for divisibility of 7 in 
        any natural number x.
    
        g(35,5,10) = 28
        g(28,5,10) = 42
        g(42,5,10) = 14
        g(14,5,10) = 21
        g(21,5,10) =  7
    */
    
    g(x,t,d)=(x+(x%d)*(t*d-1))/d;
    
    /* Find_t( x = Any natural number that is divisible by s,
               s = The divisor the search is being done for,
               d = The modulus restriction ).
    
        Returns all possible t values.
    */
    
    Find_t(x,s, d) = {
        V=List();
        
        for(t=2,d-1,
            C = factor(g(x,t,d));
            for(i=1,matsize(C)[1],if(C[i,1]==s, listput(V,t))));
            
        return(V);
    }   
    

    One thing that I noticed almost right away, regardless what d is, it seems to always work when s is prime, but not when s is composite.

    Too tired…Pains too much…Have to stop…But still…interesting.



  • Not sure, (“Older and a lot more decrepit” doesn’t mean “younger an a lot more mentally sound”, heh. Do wish I could change that, but meh, I can’t).

    Anyway, I did find a method similar to what you wrote, so I can redefine it in your terms.

    A base 20 number is divisible by 7 if the difference between 8 times the last digit and the remaining digits is divisible by 7.

    Ok, a little description on a base 20 number (Think Mayan and Nahuatl/Aztec numbers). 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19 should be considered single digits. So a base 10 number, 7*17 = 119 (1*10^2+1*10+9), would be 7*17 = 5:19 in a base 20 system (5*20+19).

    • is 1:8 divisible by 7? (28 in base 10). 8*8 = 3:4. 3:4-1 = 3:3
      • is 3:3 divisible by 7? 8 * 3 = 1:4. 1:4 - 3 = 1:1 (1*20+1 = 21).
    • is 9:2 divisible by 7? (182). 2*8 = 16. 16-9 = 7 Check.

    I’ll just leave that there. So a long weird way of saying, yes, that’s pretty much my reasoning, but not exactly at the same time. As the first message included the base 20 numbers divisible by the base 20 single digits 7, 13, and 17. (Hopefully that came off a little better).

    (Note: Saying “base 20 number[s]” is not important overall. Just being overly descriptive to differentiate between base 10 digits and base 20 digits).