ma103bpracticeexam1

# ma103bpracticeexam1 - MATH 103B PRACTICE EXAM#1 No notes...

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1 MATH 103B – PRACTICE EXAM #1 No notes, books, computers, cell phones, head phones, cylons. Each problem is worth the same number of points. 1) a) Define prime and greatest common divisor of 2 integers a,b. Give examples. b) State and prove Euclid's Lemma. c) State and prove the fundamental theorem of arithmetic. 2) a) State and prove the pigeonhole principle. b) Let p be a prime. Look at the function f: p p defined by f(x mod p) = ax (mod p), for some integer a not divisible by p. Show that this function is 1-1. Deduce from a) that it is onto. c) Show that

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ma103bpracticeexam1 - MATH 103B PRACTICE EXAM#1 No notes...

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