Wednesday

October 22, 2014

October 22, 2014

Posted by **Matt** on Wednesday, July 15, 2009 at 11:27pm.

thanx

- Maths -
**MathMate**, Thursday, July 16, 2009 at 6:38amWe will examine the sum of cubes of two numbers, A aand B. Without losing generality, we will further assume that

A=2^{n}X and

B=2^{n+k}Y

where

X is not divisible by 2

n is a positive integer and

k is a non-negative integer.

A^{3}+B^{3}

=(A+B)(A^{2}-AB+B^{2})

=2^{n}(X + 2^{k}Y) 2^{2n}(X^{2}- 2^{k}XY + 2^{2k}Y²)

=2^{3n}(X + 2^{k}Y) (X² - 2^{k}XY + 2^{2k}Y²)

Thus A^{3}+B^{3}has a factor 2^{3n}, but not 2^{3n+1}since X is not divisible by 2.

Since 10^{3n+1}requires a factor of 2^{3n+1}, we conclude that it is not possible that

10^{3n+1}=A^{3}+B^{3}

- Maths -
**Jon Zhan**, Monday, August 3, 2009 at 8:47pmNice Answer, But Please Try To Use (Mod)

That Way Is Easier

- Maths -
**Sean**, Monday, August 17, 2009 at 6:01amHey, Your ANSWER is corrupt, cause it doesnt really explain anything! Try to make it more clear.

SY

**Answer this Question**

**Related Questions**

math - Prove that a number 10^(3n+1) , where n is a positive integer, cannot be ...

maths - can you answer this question: prove that a number 10^(3n+1), where n is ...

math - can you answer this question in a different and more logical way than ...

discrete math - 1)prove that if x is rational and x not equal to 0, then 1/x is ...

MATH - Find the only positive integer whose cube is the sum of the cubes of ...

math, algebra - 2a+2ab+2b I need a lot of help in this one. it says find two ...

math - Which statement is true? A.The sum of two positive integers is sometimes ...

Math - Paulo withdraws the same amount from his bank account each week to pay ...

maths - Let σ(n) be the sum of the positive divisors of an integer n and &#...

algebra - The positive integer 4 can be represented as a sum of 1's or 2's in ...