I like addition

Number Theory Level 3

Find the sum of all integers n n such that n 2 + 97 n \frac { { n }^{ 2 }+97 }{ n } is a positive integer.


The answer is 98.

Swapnil Maiti by Swapnil Maiti , 19, India

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1 solution

Rawan Medhat
Sep 20, 2015

since n 2 + 97 n \frac { { n }^{ 2 }+97}{n} = n n + 97 n \frac { 97 }{ n }

since 97 is prime number

hence 1 and 97 are the only divisors

hence the answer = 97 +1 = 98 \boxed { 98 }

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