Number Theory


Conjecture on 3-Carmichael Numbers of the Form (4h+3)(4j+1)(4k+3)

Authors: Marius Coman

In this paper I conjecture that for any 3-Carmichael number (absolute Fermat pseudoprime with three prime factors, see the sequence A087788 in OEIS) of the form (4*h + 3)*(4*j + 1)*(4*k + 3) is true that (k – h) and j must share a common factor (sometimes (k – h) is a multiple of j). The conjecture is probably true even for the larger set of 3-Poulet numbers (Fermat pseudoprimes to base 2 with three prime factors, see the sequence 215672 in OEIS).

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[v1] 2017-01-24 02:35:20

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