On Period of the Sequence of Fibonacci Polynomials Modulo 𝑚

Table 2

Periods of the sequence of Fibonacci polynomials modulo 𝑝.

𝑝	𝑘(𝑝)	ℎ𝐹(𝑥)^𝑝	Result
2	3	6	ℎ𝐹(𝑥)^2=2𝑘(2)
7	16	112	ℎ𝐹(𝑥)^7=7𝑘(7)
37	76	2812	ℎ𝐹(𝑥)^37=37𝑘(37)
103	208	21424	ℎ𝐹(𝑥)^103=103𝑘(103)
181	90	16290	ℎ𝐹(𝑥)^181=181𝑘(181)
241	240	57840	ℎ𝐹(𝑥)^241=241𝑘(241)
373	748	279004	ℎ𝐹(𝑥)^373=373𝑘(373)
653	1308	854124	ℎ𝐹(𝑥)^653=653𝑘(653)
853	1708	1456924	ℎ𝐹(𝑥)^853=853𝑘(853)