Posted by **Help** on Wednesday, May 12, 2010 at 7:33pm.

Use mathematical induction to prove that 5^(n) - 1 is divisible by four for all natural numbers n. Hint: if a number is divisible by 4, then it has a factor of 4. also, -1 = -5 +4

This is a take home test so I don't want the answer because I want to know how to do it.

this is what I have done so far.

1. prove P(1) is true:

5^(1) -1 = 4 which is divisible by four so this checks

2. prove P(k) is true:

5^(k) - 1 is divisible by 4

5^(k) - 1 = 4(m) where m is some number

3. P(k+1):

5^(k+1) - 1 =4( ____ )

from here I have no idea what to do..if someone could help me with a hint or something that would be great....

- Math -
**edwin**, Thursday, June 17, 2010 at 2:35am
5^(k+1) - 1 =4(m+1)

## Answer This Question

## Related Questions

- Algebra ASAP - so this is a fill in on a worksheet and I am having difficulty as...
- Discrete Math - Use mathematical induction to prove the truth of each of the ...
- math - Use mathematical induction to show that 3n + 7n − 2 is divisible by...
- Discrete Math - Use mathematical induction to prove the truth of each of the ...
- Math - Use mathematical induction to prove that 2^(3n) - 3^n is divisible by 5 ...
- Calculus - Use mathematical induction to prove that each proposition is valid ...
- Math - The question is this: You know that a number is divisible by 6 if it is ...
- Algebra - Prove by mathematical induction that 3^(3n+1) + 2^(n+1) is divisible ...
- MATHS - prove by mathematical induction that 7^n+4^n+1 is divisible by 6
- maths - prove by mathematical induction that 7n+4n+1 is divisible by 6

More Related Questions