Question 410576
any number exactly divisible by 2 is an even number (result is an integer).


any number that is not exactly divisible by 2 is an odd number (result is not an integer).


1 is odd
3 is odd
5 is odd


2 is even
4 is even
6 is even


if the number ends in 1,3,5,7,9, then the number is odd.


if the number ends in 0,2,4,6,8, then the number is even.


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an odd number times an odd number will always be an odd number.


example:


501 is odd (ends in 1)
733 is odd (ends in 3)


501 * 733 results in a number that ends in 3 which is odd (367233).


367233 / 2 = 183616.5 which is not an integer.


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an odd number times an even number will always be an even number.


example:


501 is odd (ends in 1)
730 is even (ends in 0).


501 * 730 results in a number that ends in 0 which is even (365730).


365730 / 2 = 182865 which is an integer.


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an even number times an odd number will always be an even number.


just take 501 * 730 and make it 730 * 501 and you get the same answer (even).


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an even number times an even number will always be an even number.


502 is even (ends in 2)
738 is even (ends in 8)


502 * 738 results in a number that ends in 6 which is even (370476).


370476 / 2 = 185238 which is an integer.


the rules are therefore:


odd * odd = odd
odd * even = even
even * odd = even
even * even = even


what this suggests is:


if n is odd, then (x-y) * n is even or odd depending on whether (x-y) is even or odd.   you get odd * odd = odd, and you get even * odd = even.


if n is even, then (x-y) * n is always even regardless of whether (x-y) is even or odd.  you get odd * even = even, and you get even * even = even.