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consecutive integers

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Source: — Problem Solving |
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Re: consecutive integers

by quant-master » Sat Aug 01, 2009 11:45 am
bfman wrote:If (x^3) - x = p, and x is odd, is p divisible by 24?

What do you guys think?
x^3-x can be written as x(x^2-1) this can further be written as (x-1)(x)(x+1) hence 3 consecutive integers since x is odd 3 consecutive integers of this form is divisible by 24
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by bfman » Sat Aug 01, 2009 12:02 pm
Yes, in every other case but 1.
If x is 1, then the product is 0 and not divisible by 24.

I might be wrong tho ???
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by scoobydooby » Sat Aug 01, 2009 12:05 pm
0 is divisible by all numbers. no number is divisible by 0
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