Using the Mathematical Induction to prove that: 3^(2n)-1 is divisible by 4, whenever n is a positive integer.

Sinead Mcgee 2021-03-01 Answered
Using the Mathematical Induction to prove that: 32n1 is divisible by 4, whenever n is a positive integer.
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Expert Answer

Jozlyn
Answered 2021-03-02 Author has 85 answers

Claim: 32n1 is divisible by 4 for nN.
We will prove this by induction.
Base step: n=1
321=8, which is divisible by 4
the result is true fir n=1.
Inductive step:
Assure that result is true for n=k
i.e. 432k1...(1)
Now, we prove that: result is true form =k+1
i.e. 432(k+1)1
Consider 32(k+1)32k9(mod4)
19(mod4)[om(i)]
32(k+1)1(mod4)
432(k+1)1
The result is true for n=k+1.
By induction,
32(n+1)1 is divisibly by 4 for nN

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