[seqfan] Are solutions x^3*(2k+1) == 1 (mod 2^n) and x^2 == (2k+1) (mod 2^n) the same

Richard J. Mathar mathar at mpia-hd.mpg.de
Tue Dec 15 11:17:51 CET 2020


Are these two sequences the same?

http://oeis.org/?q=id:A323556|id:A323553
1,1,3,1,3,5,7,1,11,13,7,9,3,5,15,1,27,29,23,25,19,21,15,17,11,13,7,9,3,5,31,1,59,29,23,25,19,53,47,49,43,13,7,9,3,37,31,33,27,61,55,57,51,21,15,17,11,45,39,41,35,5,63,1,123,93,23,25,83,53,47,49,43,13,71,73,3,101,95,97,91,61,119,121,51,21,15,17,11,109,39,41,99,69,63,
1,1,3,1,3,5,7,1,11,13,7,9,3,5,15,1,27,29,23,25,19,21,15,17,11,13,7,9,3,5,31,1,59,29,23,25,19,53,47,49,43,13,7,9,3,37,31,33,27,61,55,57,51,21,15,17,11,45,39,41,35,5,63,1,123,93,23,25,83,53,47,49,43,13,71,73,3,101,95,97,91,61,119,121,51,21,15,17,11,109,39,41,99,69,63,

Are these two sequences the same?
http://oeis.org/?q=id:A323555|id:A323554
1,1,3,1,3,5,7,1,3,5,7,9,11,13,15,1,19,21,7,9,27,29,15,17,3,5,23,25,11,13,31,1,19,21,39,41,59,61,15,17,35,37,55,57,11,13,31,33,51,53,7,9,27,29,47,49,3,5,23,25,43,45,63,1,83,21,103,105,59,125,79,81,35,101,55,57,11,77,31,33,115,53,7,9,91,29,111,113,67,5,87,89,43,109,63,
1,1,3,1,3,5,7,1,3,5,7,9,11,13,15,1,19,21,7,9,27,29,15,17,3,5,23,25,11,13,31,1,19,21,39,41,59,61,15,17,35,37,55,57,11,13,31,33,51,53,7,9,27,29,47,49,3,5,23,25,43,45,63,1,83,21,103,105,59,125,79,81,35,101,55,57,11,77,31,33,115,53,7,9,91,29,111,113,67,5,87,89,43,109,63,



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