anonymous
  • anonymous
Theory of Numbers: If n is element of Z, prove that (4^n - 1) is divisible by 3.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
This took me awhile. I used mathematical induction. So we prove it works for 1: 4^1-1=3 which is divisible by 3. Then we assume it works for 4^n-1 and check if it then works for 4^(n+1)-1 So 4^(n+1)-1=4(4^n-1)+3 Since we assume 4^n-1 is divisible by 3, lets write it as 3a So 4(3a)+3. 3(4a+1). This is a factor of 3 and therefore divisible by 3
anonymous
  • anonymous
Well we assume it works or n and check if it then works for (n+1)

Looking for something else?

Not the answer you are looking for? Search for more explanations.