Question

Show that f(n) = n^2 - n + 17 is prime for n = 0, 1, 2, ..., 16. Show, however, that f(17) is not prime. Which step of proof by induction does this counterexample show is necessary?

Name: Show that f(n) = n^2 - n + 17 is prime for n = 0, 1, 2, ..., 16. Show, however, that f(17) is not prime. Which step of proof by induction does this counterexample show is necessary?
Uploaded: 2023-05-18T21:49:56-08:00
Duration: 1 min 46 s
Channel: Hoan Nguyen
Description: Show that f(n) = n^2 - n + 17 is prime for n = 0, 1, 2, ..., 16. Show, however, that f(17) is not prime. Which step of proof by induction does this counterexample show is necessary?

          Show that f(n) = n^2 - n + 17 is prime for n = 0, 1, 2, ..., 16. Show, however, that f(17) is not prime. Which step of proof by induction does this counterexample show is necessary?

Show that f(n) = n^2 - n + 17 is prime for n = 0, 1, 2, ..., 16. Show, however, that f(17) is not prime. Which step of proof by induction does this counterexample show is necessary?

Added by Christy L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Hoan Nguyen

05/18/2023

Step 1

To do this, we will use the induction hypothesis and prove that f(n) is not prime for n=0,1,2,...,16. Since f(n) is not prime for n=0,1,2,...,6, it follows that f(n) is not prime for n=7. Since f(n) is not prime for n=7, it follows that f(n) is not prime for Show more…

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