There are no two consecutive even numbers whose sum is 100. It is easily proved.
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No solution...
101
None exist. 100 is an even number and two consecutive integers can only add up to an odd number. This is because only 2 evens can add up to an even number and no two even numbers are consecutive. (or two odds, but no two odd numbers are consecutive either)
They are 2n+2
49, 51