# 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.