In this paper, we find patterns and count the number of distinct generalised Fibonacci sequences under modular arithmetic. We will start with the repetition of the normal Fibonacci sequence modulo an integer, m, where m is greater than or equal to two and make connections to its dependency on the prime factorisation of m. We will then extend the complexity of the problem into generalised Fibonacci sequences with different starting values. Finally we will present some interesting observations that are still open problems.

Author Bio

Connor produced the paper whilst studying at Concordia University of Edmonton in Canada on an exchange program during the 2018-2019 academic year. Connor has since completed his mathematics undergraduate degree at Coventry University in the United Kingdom and has commenced his Master's degree in mathematics at the University of Lethbridge in Canada.

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