A number theory problem by Syed Baqir

Number Theory Level 3

Find all sets of positive integers a, b and c with a ≤ b ≤ c a\leq b \leq c that satisfy the equation.

1 a + 1 b + 1 c = 1 \frac1a + \frac1b + \frac1c=1

Find the sum of all such possibilities, IE ∑ a i + b i + c i \sum a_i + b_i + c_i .


The answer is 30.

Syed Baqir by Syed Baqir , 24, Cyprus

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1 solution

Syed Baqir
Aug 24, 2015

Possible solutions are: (3 , 3, 3) ; ( 2, 3, 6 ) ; ( 2,4 ,4) Hence sum of them are 30

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Why are these all of the possible solutions?

Calvin Lin Staff - 5 years, 9 months ago

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It is because of searching step by step i.e. set a =1 and see it donot works then go to 2 and similarly when reached 3 then go to finding b which will be 3 as less then equal to 3 will not satisfy, and hence continue .. . .. .

Syed Baqir - 5 years, 9 months ago

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If so, that needs to be stated in your solution.

Not all of us are mind readers. We are only able to judge your solution based on what you have written down. Currently, it seems that you got "lucky" with finding some solutions. You have not justified why these are all of the possible solutions.

Calvin Lin Staff - 5 years, 9 months ago

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