MATH 2390 Midterm: MATH 2390 Kennesaw State sp2015Exam3solutions
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Remember that writing and correct use of notation are very important. 5| 33n 1 2n 1 for every positive integer n. The statement that we want to prove is true for all integers n 1 is. P 5 : 5|85 and this is certainly true. Now we want to prove that if k 1 then the truth of p k implies the truth of p k 1 . Thus suppose that k 1 and that p k is true. Since 5| 33k 1 2k 1 (because we are assuming that p k is true) and 5|25 then. 5| 33k 4 2k 2 which means that p k 1 is true. Therefore for all k 1 the implication. We have now proved that p k is true for all n 1: use the euclidean algorithm to compute gcd 1512, 980 . All of the steps must be shown in detail.
