Math
posted by Help .
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....

5^(k+1)  1 =4(m+1)
Respond to this Question
Similar Questions

Math
The question is this: You know that a number is divisible by 6 if it is divisible by both 3 and 2. So why isn't a number divisible by 8 if it is divisible by both 4 and 2? 
Calculus
Use mathematical induction to prove that each proposition is valid for all positive integral values of n. 5^n + 3 is divisible by 4. 
Discrete Math
Use mathematical induction to prove the truth of each of the following assertions for all n ≥1. n³ + 5n is divisible by 6 I really do not understand this to much. This is what I have so far: n = 1, 1³  5(1) = 6, which is divisible … 
Discrete Math
Use mathematical induction to prove the truth of each of the following assertions for all n ≥1. 5^2n – 2^5n is divisible by 7 If n = 1, then 5^2(1)  2^5(1) = 7, which is divisible by 7. For the inductive case, assume k ≥ … 
Math
Use mathematical induction to prove that 2^(3n)  3^n is divisible by 5 for all positive integers. ThankS! 
Algebra
Prove by mathematical induction that 3^(3n+1) + 2^(n+1) is divisible by 5 
math
Use mathematical induction to show that 3n + 7n − 2 is divisible by 8 for all n 1. [Hint: 7n + 1 is divisible by 2.] 
Algebra ASAP
so this is a fill in on a worksheet and I am having difficulty as the ones I inserted are incorrect can anybody help me how to do it all, sorry it's a long problem. Show that 3^2n − 1 is divisible by 8 for all natural numbers … 
Mathematical Induction
Use mathematical induction to prove that the following is true. 8+11+14...+(3n+5)=1/2n(3n+13), for all n in the set of natural numbers. 
number theory
The values A,B,C, and [(A/B)+C], are all integers which are divisible by 3. Then, which of the following statements must be true: A is divisible by 9 B is divisible by 9 C is divisible by 9 A and B are both divisible by 9 A,B,and C …