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Full-Text Articles in Number Theory
An Exploration Of The Use Of The Fibonacci Sequence In Unrelated Mathematics Disciplines, Molly E. Boodey
An Exploration Of The Use Of The Fibonacci Sequence In Unrelated Mathematics Disciplines, Molly E. Boodey
Honors Theses and Capstones
No abstract provided.
Pascal's Triangle Modulo N And Its Applications To Efficient Computation Of Binomial Coefficients, Zachary Warneke
Pascal's Triangle Modulo N And Its Applications To Efficient Computation Of Binomial Coefficients, Zachary Warneke
Honors Theses
In this thesis, Pascal's Triangle modulo n will be explored for n prime and n a prime power. Using the results from the case when n is prime, a novel proof of Lucas' Theorem is given. Additionally, using both the results from the exploration of Pascal's Triangle here, as well as previous results, an efficient algorithm for computation of binomial coefficients modulo n (a choose b mod n) is described, and its time complexity is analyzed and compared to naive methods. In particular, the efficient algorithm runs in O(n log(a)) time (as opposed to …