Posted by m on Thursday, July 23, 2009 at 7:18am.
can you answer this question in a different and more logical way than this method below:
we will examine the sum of cubes of two numbers, A and B. Without losing generality, we will further assume that
A=2nX and
B=2n+kY
where
X is not divisible by 2
n is a positive integer and
k is a nonnegative integer.
A3+B3
=(A+B)(A2AB+B2)
=2n(X + 2kY) 22n(X2  2kXY + 22kY²)
=23n(X + 2kY) (X²  2kXY + 22kY²)
Thus A3+B3 has a factor 23n, but not 23n+1 since X is not divisible by 2.
Since 103n+1 requires a factor of 23n+1, we conclude that it is not possible that
103n+1=A3+B3
The question is prove that a number 10^(3n+1), where n is a positive integer, cannot be represented as the sum of two cubes of positive integers.
Thanks> please explain in full steps and in the most logical order
Thanks once again

math  MathMate, Thursday, July 23, 2009 at 8:09am
The proof does look clumsy. It is however a little easier to follow if the exponents are displayed correctly. See the original version here:
http://www.jiskha.com/display.cgi?id=1247714839

math  Jon Zhang, Monday, August 17, 2009 at 5:57am
Dude, it's going to be due in like three days. Do it yourself.

math  Sean, Tuesday, August 18, 2009 at 6:41am
it's due in two days, lol
SY
Answer This Question
Related Questions
 maths  can you answer this question: prove that a number 10^(3n+1), where n is ...
 Math  James and his friends rolled two fair number cubes 500 times and recorded...
 Math  Makoto and his friends rolled two fair number cubes 500 times and ...
 Math  I have to find the relationship between these sequences, and express a ...
 math  Two standard numbers cubes are thrown. Given that one of the cubes shows ...
 Math  Makoto and his friends rolled two fair number cubes 500 times and ...
 Simple Math  Two eightsided number cubes are thrown. Given that one of the ...
 Probability  Makoto and his friends rolled two fair number cubes 500 times and ...
 Simple math  Two standard number cubes are thrown. Given that one of the cubes ...
 Math  Suppose that you have three different length of linking cubes as shows ...
More Related Questions