Question 410576: what is (x-y)n when n is odd
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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