LAST EDITED ON Feb-27-01 AT 00:05 AM (EST)

>i think the inequation
>
>N1 >= N3 * N7 is incorrect.
>
>If you take the product of
>a pair of divisors, you
>might get a number which
>is higher than the considered
>positive integer.
>
>Am I wrong?
>

The simplest way to check whether you are or not is to give an example. Do you have one? Do you have an example in which

N1 < N3·N7?

This may be the case when a number N has three divisors a, b, c such that

a·b ends in 3
a·c ends in 7
a2·b·c > N

How this may happen? For example, a may end in 1, b in 3, c in 7. Or, a may end in 7, b in 9, c in 1. Or ...

In all cases, what you lose by having a2·b·c greater than N, you gain by having one of a, b, or c end in 1. The argument must be made more accurate because this line of reasoning must also account for a possibility that one of a, b, or c will be composite.

But you are right, I have not thought of such a possibility.

The inequality N1 => N3·N7, however, I am sure is correct.