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# How to prove number is divisible by four?

Topic: Homeworks qs programming
June 17, 2019 / By Basmath
Question: I'm studying Precalculus, and I just learned how to do inductive proofs this lesson. However, all homework questions up to this point have an equation already laid out for me that I am supposed to prove. Then I came to this question: Q. Show that 5^n - 1 is divisible by 4 for all natural numbers n. (Read: 5 to the power of n, minus 1.) I do not ask that someone would prove this for me, but I would appreciate it if someone could give me an idea of what kind of equation it is I am trying to prove. I know in programming the modulus operator is used, or bitwise operators, to determine if some number is divisible by another, but I don't know how to do that with simple mathematics. (There is no similar example in the lesson material, although it could be I overlooked something in an earlier lesson.)

## Best Answers: How to prove number is divisible by four?

You don't need to use modulus operators, but just induction. First show that 5^n - 1 is divisible by 4 when n = 1. Then show that if 5^n - 1 is divisible by 4, then it follows that 5^(n+1) - 1 is divisible by 4. Assume that 5^n - 1 = 4k where k is a natural number. Solve for 5^n and plug the result into 5^(n+1) - 1 (notice that 5^(n+1) = (5^n)*(5))
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