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#1 2005-11-03 07:03:11
- juukii
- Guest
Hard
We have p > 3 where "p" is number first and a,b,c which are all-out and positive and we know that a + b + c = p + 1
and a³ + b³ + c³ - 1 is divisible by "p".
Prove that one of a,b or c equal 1
#2 2005-11-03 07:40:51
- MathsIsFun
- Administrator
Offline
Re: Hard
I have an idea for a start.
Using: a³ + b³ + c³ - 1 is divisible by "p"
Perhaps only a³ + b³ can be divisible by p, so subtracting 1 requires adding 1, and that is the c³ term
Also:
a + b + c - 1 = p
( a³ + b³ + c³ - 1 ) / ( a + b + c - 1 ) = whole number
That is as far as I have got, and I have to go do something else now.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
