Question

Show that 6^n can't end with 2 for any integer n.

Answer 1

❗❗ solution ❗❗

To show :

That 9^n can't end with 2 for any integer n.

Proof:

Let, p(n) denotes the statement that 9^n cannot end with 2 for any positive integer n.

For n=1,

p(1): 9¹=9, not ended with 2.

Let us assume that p(n) is true for n=k

i.e., 9^k can not ended with 2.

For n=k+1,

p(k+1): 9^{k+1}=9^k.9

which can not be ended with 2.

since 9^k is not ended with 2.

Now p(1) is true and p(k+1) is true if p(k) is true.

Then by the principle of mathematical induction 9^n can not be ended with 2 for any positive integer n.

For example :

9¹ = 9

9² = 81

9³ = 729

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