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px + py =xy
- px -py +xy=0
p^2 - px -py +xy =p^2 [ adding p^2 both sides ]
p(p-x) -y(p-x)=p^2
(p-y) (p-x) =p^2
Now , think (p-y) as A and (p-x) as B
So , A*B = p^2
Now , if anybody asks u the number of solutions of this solution .
Then It will make U common sense that the number of divisors will be unique solutins Because Look At this . Let's think p^2 =36
So solutions are (value of A and B)
a * b
1*36=36
2*18=36
3*12=36
4*9=36
6*6=36
a * b
36*1=36
18*2=36
12*3=36
9*4=36
Total 9 unique solutions .
Now , put n! in p So , U have to find out the number of divisors of (n!)^2 . That's all !!!
Hope it helps
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Let's take a look here ,
(1/x) + (1/y) =(1/n!) number of solutions
let's n! as p okk ? Now ..
(1/x) + (1/y) =(1/p)
(x+y)/(xy) = (1/p)