Darrell
Posts:
251
Registered:
12/6/04


Re: smallest positive integer
Posted:
Sep 5, 2007 7:13 PM


"Michael J Hardy" <mjhardy@mit.edu> wrote in message news:46ded55f$0$483$b45e6eb0@senatorbedfellow.mit.edu... > Darrell (dr6583@comcastsnip.net) wrote: > >> For argument sake I will assume a!=b. Since the smallest positive >> integer >> is 1, you can always make abk=1 by letting ab=1 and k=1. IOW, >> a=b+1 >> or b=a+1 with k=+/ 1 >> accordingly. > > > That is nonsense. You can't just "let a  b = 1. > a and b are given. The answer depends on them. > > E.g., if a = 20 and b = 3, then a  bk = 20  3k. In that case, > the integers of the form a  bk are those of the form 20  3k, > namely 20, 17, 14, 11, 8, 5, 2, 1, 4, ... etc. (and also 23, 26, > 29,...). The smallest positive integer among those is 2, and the > value of k that achieves it is 6. > > The answer depends on a and b, so you've got to say what function > of a and b it is (I've given the answer in only one case).  Mike Hardy > >
Perhaps you should read the rest of the thread where I already retracted my response.
 Darrell

