On Period of the Sequence of Fibonacci Polynomials Modulo 𝑚

Table 1

Fibonacci polynomials	Coefficient array
𝐹0(𝑥)=0	0
𝐹1(𝑥)=1	1
𝐹2(𝑥)=𝑥	1
𝐹3(𝑥)=𝑥^2+1	1	1
𝐹4(𝑥)=𝑥^3+2𝑥	1	2
𝐹5(𝑥)=𝑥^4+3𝑥^2+1	1	3	1
𝐹6(𝑥)=𝑥^5+4𝑥^3+3𝑥	1	4	3
𝐹7(𝑥)=𝑥^6+5𝑥^4+6𝑥^2+1	1	5	6	1
⋮	⋮	⋮	⋮	⋮