Hi,
I did a cursory check of the topics in this forum and I couldn't find one that addressed my question.
If I've missed it, I'd appreciate the link.
I just purchased the MGMAT Number Properties book (which has been really helpful), but when I was reviewing one of their examples on divisibility, I was still unsure of how they arrived at their solution.
The question:
If x^3 - x = p, and x is odd, is p divisible by 24?
The solution:
x(x^2 -1) => x(x+1)(x-1) => these are consecutive integers, so reorder:
(x-1) x (x+1)
The book goes on to prove that p is divisible by 24, b/c if x is odd then (x-1) & (x+1) are even.
Therefore (x-1) will be divisible by 2 b/c it is even, & (x+1) is div. by4.
I follow this logic but doesn't this assume that x is an odd integer that is greater than 1? Which I don't think the quesiton specifies.
Am I missing something?
Thanks in advance.
I did a cursory check of the topics in this forum and I couldn't find one that addressed my question.
If I've missed it, I'd appreciate the link.
I just purchased the MGMAT Number Properties book (which has been really helpful), but when I was reviewing one of their examples on divisibility, I was still unsure of how they arrived at their solution.
The question:
If x^3 - x = p, and x is odd, is p divisible by 24?
The solution:
x(x^2 -1) => x(x+1)(x-1) => these are consecutive integers, so reorder:
(x-1) x (x+1)
The book goes on to prove that p is divisible by 24, b/c if x is odd then (x-1) & (x+1) are even.
Therefore (x-1) will be divisible by 2 b/c it is even, & (x+1) is div. by4.
I follow this logic but doesn't this assume that x is an odd integer that is greater than 1? Which I don't think the quesiton specifies.
Am I missing something?
Thanks in advance.
Last edited by srk228 on Tue Aug 17, 2010 9:12 pm, edited 1 time in total.
