SOLUTION: The square of the sum of two positive, consecutive, even numbers exceeds the sum of their squares by 336. Find the numbers.

You are given

 -  = 336,    (1)

which is equivalent to

 = 336,   or

2xy = 336,   or   xy =  = 168,


where x and y are integer numbers.


So, any pair of integers with xy = 168 is the solution to equation (1).


x     y

1     168
2      84
3      56
4      42
6      28
8      21
12     14


and all reverted pairs,  and all the pairs with opposite numbers.


Of them, only the pair  (12,14)  represents  consecutive positive even integers.