show that for any natural number n, the digit in units place of 3^n cannot be even
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Step-by-step explanation:
Use induction on the exponent: The last digit is either 1, 3, 7 or 9. If 1 or 3, multiplying a power of 3 will not change the evenness of the second last digit. If 7 or 9, multiplying will result in a carry over of 2, which again does not change the evenness of the second last digit.
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