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The Factorisation of Large Integers

Published online by Cambridge University Press:  15 September 2017

C. G. Paradine
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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

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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.