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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 -

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

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