Please help me with this problem>__<;?

When s = 0
t = 14 , r = 13
( r , s , t ) = ( 13 , 0 , 14 )

When s ≠ 0
rs + t = 14 ..... (1)
r + st = 13 ..... (2)

by (1) , rs = 14 - t
by (2) , st = 13 - r
Since s ≠ 0 ,
rs / st = r / t = (14-t) / (13-r)
13r - r^2 = 14t - t^2
13r - 14t = r^2 - t^2
13r - 13t - t = ( r + t )( r - t )
13( r - t ) - t = ( r + t )( r - t )

If r = t ,
0 - t = 0
t = 0 , substitute into (2)
r = 13 , substitute into (1)
13s = 14
s = 14/13 , not an integer

If r ≠ t
13( r - t ) - t = ( r + t )( r - t )
13 - t/( r - t ) = r + t
t/( r - t ) = 13 - r - t = some integer m
t = ( r - t )m = rm - tm
t(1+m) = rm
t : r = m : (m+1)

Since t , r , m are integers, we have
t = mn and r = (m+1)n , for some integer n
Substitute into (1) & (2) , we get
(m+1)ns + mn = 14
(m+1)n + smn = 13

mns + ns + mn = 14 ..... (3)
mn + n + mns = 13 ..... (4)
(3) - (4) , we have
ns - n = 1
n( s - 1 ) = 1
s - 1 = 1/n
Since s-1 is an integer, so is 1/n.
Hence n = 1
s - 1 = 1
s = 2 , substitute into (1) & (2) , we get
2r + t = 14
r + 2t = 13
And the solution is r = 5 , t = 4
( r , s , t ) = ( 5 , 2 , 4 )

Ans:
( r , s , t ) = ( 13 , 0 , 14 ) or ( 5 , 2 , 4 )