For every positive integer n, prove that `7^n-3^n`is divisible by 4.

1.	For every positive integer n, prove that `7^n-3^n`is divisible by 4.
Answer» `7^n - 3^n = 4t` a) `n=1` b) `n=k, n=k+1` a) n=1, LHS`7^n - 3^n= 7-3 = 4` RHS`= 4` b) Assumption `n=k` `7^n - 3^n = 4k` `n= k+1` LHS: `7^(k+1) - 3^(k+1)` `= 77^k - 33^k` `= 47^k + 3 7^k - 3*3^k` `= 4(7^k) + 4t` `= 4(7^k + t)` Answer

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