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