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Material Type: Exam; Class: Introduction to Proofs Via Number Theory; Subject: Mathematics; University: Western Washington University; Term: Winter 2005;
Typology: Exams
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Put your answers in the space provided. Show your reasoning. Calculators are to be used when appro-priate. The maximum score on the test is 30 points.
7a. 1 point Exhibit primes larger than 20 of the form 6 k − 1 and 6 k + 1 Answers
7b. 1 point If p > 3 is a prime, then prove that p is either of the form 6 k − 1 or 6 k + 1.
7c. 2 points If p > 3 is a prime, then prove that p^2 + 2 is always composite.