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

Q: What is the sum of two even consecutive integers the equal 100?

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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

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The integers are 99, 100 and 101. There is also a set of consecutive even integers whose sum is 300. That set is 98, 100 and 102.

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

The GCF of consecutive integers is 1.

49, 51

The average of the three integers is going to be -306/3 = -102. Therefore, taking one even integer from either side, -306 = (-100) + (-102) + (-104)

All of them from 45 to 99 ... 55 integers.

99, 100, and 101

100

49 and 51