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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)
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).
Awesome answer .....
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