Number Theory


Formula to Generate a Set of Poulet Numbers from a Poulet Number P and Its Factor D Lesser Than Sqr P

Authors: Marius Coman

In this paper I make the following observation: Let d be a factor (not necessarily prime) of the Poulet number P such that d < sqr P and m the least number such that m*d*(d – 1) > (P – 1)/2. Let n be equal to P – m*d*(d – 1). Then often exist a set of Poulet numbers Q such that Q mod(m*d*(d – 1)) = n. For example, for P = 2047 = 23*89 and d = 23, where d < sqr 2047, the least m such that m*23*22 > (P – 1)/2 is equal to 3 (1518 > 1023, while, for 2, 1012 < 1023); so, n = 2047 – 3*23*22 = 2047 – 1518 = 529 and indeed there exist a set of Poulet numbers Q such that Q mod 1518 = 529; the formula 1518*x + 529 gives the Poulet numbers 2047, 6601, 15709, 30889 (...) for x = 1, 4, 10, 20 (...).

Comments: 2 Pages.

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Submission history

[v1] 2017-04-23 12:08:04

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