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The number field sieve is the most efficient known algorithm for factoringlarge integers that are free of small prime factors. For the polynomialselection stage of the algorithm, Montgomery proposed a method of generatingpolynomials which relies on the construction of small modular geometricprogressions. Montgomery's method is analysed in this paper and the existenceof suitable geometric progressions is considered.

Montgomery's method of polynomial selection for the number field sieve