Originally Posted by

**ProtoflareX** I am having trouble understanding how to "prove" the following statement: "Prove by Direct Method: If x is an even integer, then x^2 - 6x + 5 is odd". What I am aware of currently is that the definition of an odd number is "n = 2k + 1", where n is the number you are trying to prove is negative and k is any integer. However, if you place 2, or 4 into the formula as x, the result is an odd, negative number, which cannot be proven odd using the definition of a negative number since there is no integer than when multiplied by 2 results in a negative number. If you place a large, even x value into the equation, then the result is a positive, odd number which can be proven odd using the definition of an odd number, but if the result of the formula is negative and odd, how do you prove that?