Problem On Fundamental Concepts of Number Theory

Let P 1 , P 2 , P 3 , . . . . , P k P_{1},P_{2},P_{3},....,P_{k} are all possible positive factors of a number n n including 1 1 and n n . It is given that P 1 + P 2 + P 3 + . . . + P k = 2018 P_{1}+P_{2}+P_{3}+...+P_{k}=2018 then i = 1 k \sum_{i=1}^{k} 1 P i \frac{1}{P_{i}} = = m n \frac{m}{n} .

Find the value of m m where m m is a positive integer.


The answer is 2018.

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1 solution

Taisanul Haque
Nov 1, 2018

As we know that factors occurred in P A I R PAIR ,So we can write

Therefore m = 2018 m=2018

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