
is to say that for any

, we can find

such that

implies

.
To that end, we have

which means that if

is given, then we can choose

; if

, then

; if

, then

.
Answer:
Let a and b integers and suppose that are even numbers. Then, exist integers k and m such that
and
.
Then,

Since, k and m are integers then n=k+m is an integer. Then, since a + b is of the form 2 by an integer n, then a + b is an even number.
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