math
posted by m .
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

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 
Dude, it's going to be due in like three days. Do it yourself.

it's due in two days, lol
SY
Respond to this Question
Similar Questions

maths
can you answer this question: 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. with out using this method at all ................................. We … 
Math
I have to find the relationship between these sequences, and express a generality. Could you help please. 1 + 3 + 5 + 3 + 1 = 3^2 + 2^2 1 + 3 + 5 + 7 + 9 + 7 + 5+ 3 + 1 = 5^2 + 4^2 1 + 3 + 1 = 2^2 + 1^2 I'm thinking sum of consecutive … 
math
Two standard numbers cubes are thrown. Given that one of the cubes shows a two, what is the probability that the sum of the numbers that come up on the two cubes is four? 
Simple Math
Two eightsided number cubes are thrown. Given that one of the cubes shows a five, what is the probability that the sum of the numbers that come up on the two cubes is six? 
Simple math
Two standard number cubes are thrown. Given that one of the cubes shows a five, what is the probability that the sum of the numbers that come up on the two cubes is five? 
Math
Makoto and his friends rolled two fair number cubes 500 times and recorded the sum of the numbers shown on the cubes each time.On 42 of the trials the sum was 10.Which of these is most likely the probability that the sum of the numbers … 
Math
Makoto and his friends rolled two fair number cubes 500 times and recorded the sum of the numbers shown on the cubes each time. On 42 of the trials the sum was 10. What will be the probability that the sum of the numbers shown on the … 
Probability
Makoto and his friends rolled two fair number cubes 500 times and recorded the sum of the numbers shown on the cubes each time. On 42 of the trials the sum was 10. What will be the probability that the sum of the numbers shown on the … 
Math
James and his friends rolled two fair number cubes 500 times and recorded the sum of the numbers shown on the cubes each time.On 42 of the trials the sum was 10.Which of these is most likely the probability that the sum of the numbers … 
maths
supose that you have three diffrent lenghts of linking cubes as shown below assume that you have as many of these lenghts as you need but you may not take them apart can you make each lenghts below using only one colour if it is possible …