The eighth even number is 16.
1. 2
2. 4
3. 6
4. 8
5. 10
6. 12
7. 14
8. 16, etc.
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If you multiply any even number by an even number, the product is an even number.
There is need for a conjecture. It is an easily proven fact that an even number minus an even number is always an even number.
Your question is incomplete. Adding an even number with an odd number will always result in an odd number. Multiplying an even number with an odd number will always result in an even number.
An odd number plus an odd number will be an even number. Odd number A is (even number + 1) Odd number B is (even number + 1) A + B = (even number + 1) + (even number + 1) = even number + even number + 2 Since all even numbers are divisible by 2 and 2 is divisible by 2, each part of the result is divisible by 2, so the sum as a whole is divisible by 2, which means it is an even number.
6 is an even number. A even number is a number which is divisible by 2 and the resulting quotient is a whole number (not a fraction). 6 is divisible by 2, making it an even number.