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Q: What are two consecutive even integers whose sum is 50?

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The consecutive integers whose sum is 51 are 16, 17, and 18.

The two even consecutive integers are: 62+64 = 126

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There are no two consecutive even numbers whose sum is 100. It is easily proved.

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The integers are 20 and 22.

There is no pair of consecutive even integers whose sum is 264 - as their average is divisible by 4, that must mean that the sum of the unit digits of each of the pair of numbers could never be a multiple of 4 - which 264 is.