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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)

290 Points
9 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,

Sathya
35 Points
9 years ago