So: n+y+ny=2008.
( 1+n)y=2008-n
y=(2008-n)/( 1+n)
y =(2008-n- 1+ 1)/( 1+n)
y=2009/( 1+n)- 1
To make y an integer, 2009/( 1+n) is an integer.
(decompose 2009 into prime factors) because 2009=7*7*4 1
So: 1+n=7 x=6, y=286.
1+n=4 1 X = 40 and Y = 48.
1+n=7*7=49 At this time, X = 48 and Y = 40.
1+n=7*4 1=287 x=286,y=6。
1+n=2009 At this time, x=2008, y=0 (not conforming to positive integer rounding).
To sum up: x=6, y=286.
x=40,y=48
x=48,y=40
x=286,y=6