On the size of modular numbers
Aviezri S. Fraenkel · 1964
An iterative matrix method for determining the size of modular numbers which includes some previous methods as special cases, is discussed. It is proved that for a certain class -and-bgr; of auxiliary matrices which includes a matrix used by Mann (Math. Comp., 15, 1961, 190-192), the method always converges. It is shown, roughly speaking, that for a certain sub-class of -and-bgr;, chances of reducing the number of iteration steps are very high if certain conditions are imposed on the moduli. If one uses numerically least residues instead of least non-negative residues, these chances appear to be further improved, whereas the conditions on the moduli are less stringent.