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If n is an odd integer then the next two consecutive odd integers are n+2 and n+4.
If n is one integer, then the consecutive integer to it is n+1, and the next is n+2 and so on.
Every integer is either even (divisible by 2) or odd (not divisible by 2). Since an even number plus 1 is odd and an odd number plus one is even, because 1 does not divide 2. We know (n + 4) is odd. The next integer is (n + 4 + 1) = (n + 5), because an odd number plus 1 is even, (n + 5) is even. The integer after (n + 5) is (n + 6), since (n + 5) we know is even, (n + 6) must be odd. Since (n + 6) is the smallest integer that is greater than (n + 4) and is odd, so (n + 6) is the next odd integer.
An even integer is a number that is a multiple of 2. If n is an even integer, the next consecutive even integers are n+2, n+4 and so on.