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# n is an integer. Is n&#9516;&#9619;1 evenly divisible by 8?

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SVP
Joined: 03 Feb 2003
Posts: 1608
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Kudos [?]: 76 [0], given: 0

n is an integer. Is n&#9516;&#9619;1 evenly divisible by 8? [#permalink]  04 Oct 2003, 07:11
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n is an integer. Is n┬▓–1 evenly divisible by 8?

(1) n┬▓–1 is evenly divisible by 2
(2) n–1 is even
Manager
Joined: 26 Aug 2003
Posts: 233
Location: United States
Followers: 1

Kudos [?]: 2 [0], given: 0

Wait, why can't (2) also give you the answer?

For example:
n = 1, (n^2 - 1) % 8 = 0
n = 3, (n^2 - 1) % 8 = 8 % 8 = 0
n = 5, (n^2 - 1) % 8 = 24 % 8 = 0
n = 7, (n^2 - 1) % 8 = 48 % 8 = 0
n = 9, (n^2 - 1) % 8 = 80 % 8 = 0
SVP
Joined: 03 Feb 2003
Posts: 1608
Followers: 6

Kudos [?]: 76 [0], given: 0

Let's discuss (2):
n┬▓–1=(n+1)(n-1)
n is odd, so (n+1) and (n-1) are consequtive even integers, their produst is evenly divisible by 8

Sorry, D is right
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