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Number Theory

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In the equation 1/j + 1/k = 2/3, both j and k are positive integers. What is the sum of all possible values for k?

Aug 16, 2021

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In the equation 1/j + 1/k = 2/3, both j and k are positive integers. What is the sum of all possible values for k?

Hello Guest!

1/j + 1/k = 2/3

$$\frac{1}{k}=\frac{2}{3}-\frac{1}{j}\\ \frac{1}{k}=\frac{2j-3}{3j}\\ \color{blue}k=\frac{3j}{2j-3}$$

$$j\in\{$$  0,  1,  2,  3 $$\}$$

$$k\in\{$$  0, -2,  4,  2 $$\}$$

The sum of all possible values for k is 4.

!

Aug 16, 2021