Author: goggy Format: TextIf we have a sequence of pairs (1,a1), (2,a2), .... , (n, an) such that the sequence a1, ... , an first increases and decreases, and the n pairs can be rearrange into: (b1, b2), (b2, b3), .... , (b{n-1}, bn), (bn, b_1).
I have this conjecture that the number of these sequences of pairs are equal to the number of irreducible polynomials over GF[2]. I kinda see that the proof goes in the direction of considering the fact that the roots of any irreducible polynomial form a single orbit under the action of the multiplicative group. How might I approach the proof?
If we have a sequence of pairs (1,a1), (2,a2), .... , (n, an) such that the sequence a1, ... , an first increases and decreases, and the n pairs can be rearrange into: (b1, b2), (b2, b3), .... , (b{n-1}, bn), (bn, b_1).
I have this conjecture that the number of these sequences of pairs are equal to the number of irreducible polynomials over GF[2]. I kinda see that the proof goes in the direction of considering the fact that the roots of any irreducible polynomial form a single orbit under the action of the multiplicative group. How might I approach the proof?