Show that for any natural number n the digit in unit place 3^n cannot be even
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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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