How to Prove that every positive integer n, 7n−3n is divisible by 4

By Team Aakash BYJU'S

For every positive integer n, 7n−3n is divisible by 4.

A. True

B. Flase

Correct Answer

A. True

Move to next slide for explanation.

Consider P(n):7n−3n is divisible by 4 Now, P(1):71−31=4

Thus, it is true for n=1 Let p(k) is true for n=K 7k−3k is divisible by 4

Now, prove that P(k+1) is true.

7(k+1)−3(k+1)=7(k+1)−7.3k+7.3k−3(k+1) =7(7k−3k)+(7−3)3k=7(4d)+(7−3)3k =7(4d)+4.3k=4(7d+3k)

Hence, P(n):7n−3n is divisible by 4 is true.

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