A162570 - OEIS

A162570

Positive integers n such that the polynomial P(n,t) = t^{2^{n-1}} * (t+1)^{2^{n-1}-1} + 1 of GF(2)[t] is irreducible, where GF(2) = {0,1} is the binary finite field with two elements.

%I #10 Aug 14 2013 14:00:55

%S 1,2,3,4,6,7,15

%N Positive integers n such that the polynomial P(n,t) = t^{2^{n-1}} * (t+1)^{2^{n-1}-1} + 1 of GF(2)[t] is irreducible, where GF(2) = {0,1} is the binary finite field with two elements.

%e For n=1 the polynomial P(1,t)=t+1 is irreducible in GF(2)[t]. For n=3 the polynomial P(3,t)=t^4(t+1)^3+1 = t^7+t^6+t^5+t^4+1 is irreducible in GF(2)[t].

%o (PARI) isok(n) = polisirreducible(Mod(1,2)*(t^(2^(n-1))*(t+1)^(2^(n-1)-1)+1)); \\ _Michel Marcus_, Aug 14 2013

%K nonn,hard,more

%O 1,2

%A _Luis H. Gallardo_, Jul 06 2009