Prove that 3^2n+7 is divisible by 8
1 answer:
Answer:
Step-by-step explanation:
If n=1 then 32n+7=16=2(8) so true when n=1
Assume true for n=k so
8|32k+7
If n=k+1
32(k+1)+7
32k+2+7
If 32n+7 is divisble by 8 then 32n+7=8A where A∈Z, and thus 32k+2+7=8B where B∈Z
32×32k+7
32×(8A)=72A
72A=8(9A)=9B
So by induction 32n+7 is divisibe by 8 ∀n∈N
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