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  • 15 Comments
Joined 1 year ago
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Cake day: June 14th, 2023

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  • I used to drink root beer out of the licorice red vines, those held up quite well. Though, the lart was around seven years ago. I haven’t seen blaok red vines in ages around these parts.

    Have no idea if the red ones would have held up. Never liked those too much, heh, and other than root beer, birch beer, I’d drink coffee instead.





  • 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.