# Find the no of solutions for 1/x + 1/y = 1/1995Ans:16

Swapnil Saxena
102 Points
12 years ago

Since it is a linear equation in two variables so there exist infinite solutions for the equation.

Sathya
35 Points
12 years ago

yes,i need the no of integral solutions

shaswat roy
19 Points
12 years ago

i think its safe to assume you want the natural number solutions.

y = 1995x/(x - 1995)

Since y is a natural number therefore we have 2 cases. First case is when (x-1995) divides 1995.This will happen when (x-1995) is a factor of 1995.So look at its prime factorization i.e 3X5X7X19.Clearly this has 16 factors therefore we will have 16 solutions for x and hence 16 solutions overall.

the other case is when (x-1995) divides x. you can check for yourself that the solutions obtained in this case yields no new solutions i.e we get the same solutions as we got in the earlier case.

Sathya
35 Points
12 years ago

zthere r only 4 solutions(factors) for x.Thn how can u saay tat it has 16 solutions?

Swapnil Saxena
102 Points
12 years ago

There r no doubt 16 solution 1,3,5,7,19,15,21,57,95,35,133,105,(35*19),(21*19),(105*19),(15*7*19).

Dont see only prime factors but also possible combination formed by multiplication of these prime factors.

Shikhar
15 Points
5 years ago
The answer the no. of factors of square of 1995
It is 27 not 16
( 1995^2 = (5*3*133)^2
No of factors = (2+1)^3