novice needing help
Hi, I just started to read about cryptography and during my readings I found a small problem probably not very hard but I just don't know how to solve it. My number theory knowledge is very limited. a = b/c and d = b/(b mod c) I would like to demonstrate that gcd(a,d) = 1 and a*d>=b for any b and c values(assuming b mod c != 0) is true or false through logical induction. Is there someone that could give me a hint ? TIA Olivier Langlois - olanglois@sympatico.ca - http://www3.sympatico.ca/olanglois Montreal, Canada
On Tue, 11 Aug 1998, Olivier Langlois wrote:
a = b/c and d = b/(b mod c)
I'm not sure what you're trying to say with this notation. Well, if by '/' you mean integer division with truncation (a la most programming languages,) then consider that 9 = 49/5 and 12 = 49/(49%5=4) And so gcd(a,d) != 1. This is my best guess as to what you're trying to say, since in number-theoretic notation these two statements don't make much sense: division is not closed on the integers, and (b mod c) is not a single integer, but an equivalence class. -Caj
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Olivier Langlois -
Xcott Craver