| Lucas sequences have been able to hold mathematician's interest over time. They have been used in the search for large primes, primality testing, and factoring numbers. More recently, Lucas sequences have taken on a role in cryptography. It is well known that the growth of Lucas sequences is exponential, but if terms in the sequence are reduced modulo n then the sequence eventually becomes periodic. This thesis is a survey of the classical development of Lucas sequences and its extention to new relations modulo prime powers. |
