Question 1094072
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You are given

{{{(x+y)^2}}} - {{{(x^2+y^2)}}} = 336,    (1)

which is equivalent to

{{{x^2 + 2xy + y^2 - x^2 - y^2}}} = 336,   or

2xy = 336,   or   xy = {{{336/2}}} = 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.
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