A number theory problem by Sutirtha Datta

Number Theory Level 3

$\frac{1}{a}+\frac{1}{b}=\frac{1}{2017}$

Find the number of ordered pairs of positive integers $(a,b)$ satisfying the equation above.

1 solution

Sutirtha Datta
Feb 4, 2017

$\frac{1}{a}+\frac{1}{b}=\frac{1}{2017}$

$\implies$ $2017a+2017b=ab$

$\implies ab-2017a-2017b+2017^2=2017^2$

$\implies (a-2017)(b-2017)=2017^2$

Now $\tau({2017^2})=3$

Hence three solutions exist

Hmmm, what do you mean by $\tau(2017^2)$ ? What does this function represent?

Pi Han Goh - 4 years, 4 months ago

Tau denotes # +ve divisors of the given no. Here 2017^2

Sutirtha Datta - 4 years, 4 months ago

How do you know the answer must be $\tau(2017^2)$ ?

Pi Han Goh - 4 years, 4 months ago