Re: A fairly simple proposition

From: Doug Goncz (dgoncz_at_aol.com)
Date: 11/14/04 

Date: 14 Nov 2004 13:20:48 GMT

Well, I recall something like if gcd(a,b,c)=1 then gcd(a+b, c-a, c-b)=1...

A counterexample woudl certainly be useful, but I'd like to hear some theory.
It's really pretty bare. Just the two conditions gcd(a,b,c)=1 and a<b<c<(a+b)
do produce c-a !== 0 (mod b) OR c-b !== 0 in my searches to c=101. But why
would that be? I haven't found a counterexample.

What's the symbol for OR? V? or \/?

Restating:

Given
0<a,b,c
a<b<c<(a+b)
gcd(a,b,c)=1

Proposition:
c-a !== 0 (mod b) \/ c-b !== 0 (mod a)

Proposition true? Counterexample? Discussion?

An alternative proposition,

a+b !== 0 (mod c) \/ c-a !== 0 (mod b) \/ c-b !== 0 (mod a)

might be true if the proposition I have made is not.

Doug Goncz
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