Zigzag polynomials, Artin's conjecture and trinomials

We begin by considering faithful matrix representations of elementary abelian groups in prime characteristic. The considered are seen to be determined up change bases a single number. Studying this number leads new family polynomials which exhibit special properties. These satisfy three term recursion and closely related zigzag zero-one sequences. Interpreting the for "prime" 1 yields classical Morgan-Voyce polynomials, form twoorthogonal families have applications study electrical resistance. Study general reveals deep connections with Fibonacci series, order appearance numbers sequence, elements cyclic groups, Artin's conjecture on primitive roots factorization trinomials over finite fields.