Advertisements

. . . but otherwise, little to report.

I’m filling in spaces where values are needed for the various columns in my nearly-complete chart of all the discrete semiprimes between 0 and 20000 whose Ascents are greater than 0; i.e., whose Ceiling Squares do not differ from them by exactly a perfect square, which enables immediate Fermat factorization.

There’s this, but it’s mainly review.

```
Characteristic polynomial corresponding to m
when m = c^2 - r,
and c = ceil( sqrt( m ) )
plus 0 or 1, as c is or is not congruent
to (m+1)/2 modulo 2, respectively:
f(x) = x^2 + 2cx + r
= x^2 + 2cx + c^2 - c^2 + r
= (x + c)^2 - m.
The least non-negative x for which f(x) is a perfect square
gives m = (x + c)^2 - n^2 for some a,
which also gives x+c+n and x+c-n as factors of m.
```

## Leave a ReplyCancel reply