Discrete Mathematics: 3. Prove: 7n -1 is divisible by 3 for n ³ 0

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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Discrete Mathematics:

3. Prove: 7n -1 is divisible by 3 for n ³ 0.

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Step 1

We need to prove that the number 7n-1 is divisible by 3 for n>0. We do this as follows:

Case-1: n=1

We have 7n-1=7-1=6=2×3 which implies that for n=1, the given number is divisible by 3.

Case-2: n>1

We can write the given number as (6+1)n-1. Now, we use the binomial expansion i.e., (a+b)n=C0nan+C1na1bn-1+C2na2bn-2+...+Cnnbn for the term (6+1)n with a=6 and b=1. 

 

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