>Something must be missing from this. Statements (i) and (ii) just don't
>work. See below for the statements.
>A counter-example for (i): Let N=28, k1=3. Let f=6k1+1 = 19. N/f leaves
>remainder 9, which is not equal to k1. However, 6N+1 which is 169, does
>have a factor of the form 6n+1, namely 13.
>What am I missing?
Thanks for pointing this out, Tom. This shows that there is a hole in the
statement of the theory. I should find a better way to state it.
Actually there is some 6k1 + 1 for which N/(6k1 + 1 leaves the remainder k1,
namely 13 = 6*2 + 1. 28 /13 leaves 2 as a remainder.
Frank also spots a mistake in the prove. This might also be true. About the
proof I am not that confident, OK.