Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-04T18:16:18.163Z Has data issue: false hasContentIssue false
  • English
  • Français

The Factorisation of Large Integers

Published online by Cambridge University Press:  15 September 2017

C. G. Paradine
Get access Rights & Permissions [Opens in a new window]

Extract

If a number N (other than an odd multiple of 2) is the product of two factors, then N = x2 – y2, where x and y are half the sum and half the difference respectively of the factors, and are integers. To determine x and y we may use the quadratic residues of small primes as follows.

Let N = a2 + b where a2 is the perfect square nearest to N.

Type
Research Article
Information
The Mathematical Gazette , Volume 19 , Issue 235 , October 1935 , pp. 267 - 273
Copyright
Copyright © Mathematical Association 1935

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

page 268 note * More strictly, N/2k - a. This makes a considerable difference if N is comparatively small.

page 269 note * The negative root of the quadratic in k gives the larger factor of N.

page 272 note * The ratio 1 to 3 is the geometric mean of the chosen ratios.