Question
The number $n^{2}-n+41$ is prime for $n=1,2, \ldots, 40 .$ Does this prove that $n^{2}-n+41$ is prime for every natural number $n ?$ Explain.
Step 1
It is given that the number $n^{2}-n+41$ is prime for $n=1,2, \ldots, 40$. We are asked to determine if this proves that $n^{2}-n+41$ is prime for every natural number $n$. Show more…
Show all steps
Your feedback will help us improve your experience
James Kiss and 88 other Precalculus educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Show that the statement "n $^{2}-n+41$ is a prime number" is true for $n=1$ but is not true for $n=41$
Sequences; Induction; the Binomial Theorem
Mathematical Induction
Prove or disprove: $n^{2}+21 n+1$ is a prime number for all natural numbers $n$
Sequences, Induction, and Probability
Find the first integer $n$ for which $n^{2}-n+41$ is not a prime number.
Precalculus Preview
A Note on Mathematical Proof; Mathematical Induction
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD