MATH 406 Study Guide - Midterm Guide: Euler Function, Reduced Residue System, Quadratic Residue

• School: University of Maryland
• Department: Mathematics
• Course: MATH 406
• Professor: All

Document Summary

Put nal answer to each problem in a box if the problem is a computation. Show all your work on these pages, using the backs for scratch paper. Reminder: is the euler phi function, (n) is the number of divisors of n, (n) is the sum of the divisors of n, and (n) is the m obius function. (pa) = pa 1(p 1), (pa) = a + 1, (pa) = pa+1 p 1 , (pa) = 1 if a = 1 and is 0 if a > 1. 1: (30 points) using euler"s theorem about congruences and powers, prove that for any integer n, 10n8. Induction is much harder, and you will not receive full credit for such a proof. Math 406: (30 points) the function is the summatory function of the identity. The identity is the summatory function of the euler function .