19 May
2018
19 May
'18
6:13 p.m.
The quartic polynomial z^4 - 2*z^3 + z^2 - 2*z + 1 factorises completely into linear factors over finite field |F_p for p in set S = { 23, 127, 137, 151, 233, 239, 281, 359, 431, 449, 487, 673, 743, 751, 911, 953, 967, 977, ... } (all members with p < 1024). Can anything constructive be said about S ? For instance, Is S infinite? Does S contain subsets of form { p | p prime & p == a (mod b) } ? What (bounds on) asymptotic density has S , if any? WFL