MATH 111 Final: STAT 111 Amherst S17Stat135 2801 29FinalLiao

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 111
• Professor: All

Document Summary

Find the smallest positive value of n such that np = o. (recall, o is the point at in nity and np = P + p + + p: (30 points) for each of the following, either prove the statement or give a counter example. (a) if p is prime, p! is never a perfect square. n times. , pr denote the rst r primes (ex. p1 = 2, p2 = 3, p3 = 5, etc. ). The number n = (p1 p2 . 1 a p 1 is a quadratic residue modulo p if a b2 (mod p) for some 1 b p 1. 1 (a) compute the sum of the quadratic residues modulo p for each prime less than 20. (b) use induction to prove that for any integer n, n. X i=1 i2 = n(n + 1)(2n + 1)