if x is an even integer, is x(x+1)(x+2) divisible by 4?

[dlou0716]

Hi,

if x is an even integer, is x(x+1)(x+2) divisible by 4?

since 0 is an even integer, the answer to the above question shouldn't be Yes as it is stated on page 86. It states 0 is an even integer on page 55.

if x^3-x=p, and x is odd, is p divisible by 24?

it doesn't say x doesn't equal to 1 or p doesn't equal to 0, so it is possible that x=1 and p=0, correct?

And a quick question regarding consecutive integers ... does it always have to start with the number 1? for example, { -1, 0, 1 } is not considered a set of 3 consecutive integers somehow?

Thank you very much!

[StaceyKoprince]

if x is an even integer, is x(x+1)(x+2) divisible by 4?

since 0 is an even integer, the answer to the above question shouldn't be Yes as it is stated on page 86. It states 0 is an even integer on page 55.

0 is, in fact, an even integer. 0 is also divisible by every number, including 4.
Think about it. What is 0/4? 0. Is that an integer? Yes. Is there any remainder? No. Therefore, 0 is divisible by 4. :)

if x^3-x=p, and x is odd, is p divisible by 24?

it doesn't say x doesn't equal to 1 or p doesn't equal to 0, so it is possible that x=1 and p=0, correct?

Yes, x could equal 1 and p could equal 0. And, as above, 0 is divisible by 24.

{-1,0,1} is, in fact, a list of consecutive integers. Whether that particular set (eg, including negative numbers of including 0) is allowed in a particular problem just depends upon the parameters of that problem.