Math homework

1/x + 1/y = 1/2016. Well, one obvious solution is:

x =4032 and y =4032!!!!!!,because

1/4032 + 1/4032 = 1/2016

1/x + 1/y  = 1/2016

I'm  assuming that x and y must be different natural numbers

We have a "formula" that says that

1/n =  1/[ n + 1]  +  1/ [n (n + 1)]

So...if n = 2016.....then   1/[ n + 1]  +  1/ [n (n + 1)]    =

1/2017 + 1 /[ (2016)(2017)]  =     get a common denominator

[2016 + 1 ] /  [ 2016 * 2017] = 

2017 / [ 2016 * 2017]  =

1/2016

So......x =  2017   and y = 2016*2017  = 4,066,272

Well, almost any multiple of 2016 of x will give you a solution for y such as :
x=6,048 and y=3,024
x=8,064 and y=2,688
x=10,080 and y =2520
............etc.

Guest is correct....I should have stated that my solution isn't unique.....!!!!

He is using the identity that, for k =1, 2, 3, 4, 5........

1/n  =

1/[k*n] +  1/ [k * n / (k -1)]   =

1 [/k*n] + [k-1] / [ k *n ]  =

[ k - 1 + 1 ] / [k*n ] =

k /[ k*n  ] =

1/n