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if x and y are both positive integer then find all ordered pair (x,y)_ such that (1/x)+(1/y)=(1/1995)

if x and y are both positive integer then find all ordered pair (x,y)_ such that (1/x)+(1/y)=(1/1995)

Grade:12

2 Answers

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

Hi Akshay,

 

This is a good Question.

Rearrange the given Equation.

 

We will have x = 1995y/(y-1995).

 

First let us prime factorise 1995.

So 1995 = 3*5*7*19.

 

So now this equation can have solutions when 1995 is divisible by y-1995.

 

So y-1995 = 1,3,5,7,19 (that is all factors taken one at a time) ------ 5 cases.

or factors taken 2 at a time, ie y-1995 = 3*5, 3*7, 3*19, 5*7, 5*19, 7*19 ----- 6 cases.

or factors taken 3 at a time, ie y-1995 = 3*5*7, 5*7*19, 7*19*3, 3*5*19 ----- 4 cases.

or factors taken all at a time, ie y-1995 = 1995 ------ 1 case.

 

So totally there would be 5+6+4+1 = 16 ordered pairs of (x,y)

 

Based on the above working you can find the ordered pairs.

 

Hope this would help.

 

Best Regards,

Ashwin (IIT Madras).

Sathya
35 Points
10 years ago

Awesome answer .....

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