This is the archived website of SI 486H from the Spring 2016 semester. Feel free to browse around; you may also find more recent offerings at my teaching page.

Problem 25

Longest-period Lehmer LCG with m=65537

Due: February 2
Points: 2

Find the parameter a that maximizes the period of a Lehmer linear congruential generator with \(m=65537\) and with any seed value. (Note: this is the smallest prime greater than \(2^{16}\).)

You obviously don't have to write out an entire sequence, but you need to explain how you know it has the maximal period.