Paul's answer

Number Theory Level 2

Given any positive integer n n , Paul adds together all the distinct factors of n n , other than n n itself. What is the smallest number apart from 2 that can never be Paul's answer?


The answer is 5.

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Julian Uy by Julian Uy , 26, Philippines

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1 solution

Julian Uy
Jan 7, 2015

If the sum were 5, then the factors would have to be 1 and 4. However if 4 is a factor of n n , then 2 is also a factor which produces a contradiction. Since 4 is the smallest number that is not prime (and not 1), it is the smallest number that produces this contradiction.

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What about 3 3 ?

Marc Vince Casimiro - 6 years, 5 months ago

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For 3, the factors of a number would be only 1 1 and 2 2 . An example of this is 4 4

Julian Uy - 6 years, 5 months ago

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oh nice, haven't thought of four

Marc Vince Casimiro - 6 years, 5 months ago

How can Paul get a sum of 2?

Calvin Lin Staff - 6 years, 5 months ago

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I have updated the answer to 5.

Those who previously answered 2 (correct answer under the previous phrasing) have been marked correct.

Calvin Lin Staff - 6 years, 5 months ago

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