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27 November, 11:48

Dad just had a birthday. Before this birthday, dividing Dad's age by 2 left a remainder of 1. How do you know that's Dad's new age is not a prime number?

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  1. 27 November, 12:06
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    Before his current birthday, when you divided by two you got a remainder of 1 which means that your father's age then was odd number. You get a remainder of 1 with any odd number by 2.

    He's now had a birthday. The way to show this is 2n + 1 for his age before his birthday. He has a birthday so his age is 2n + 1 + 1 = 2n + 2 which is an even number and therefore not prime.
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