Monday

March 30, 2015

March 30, 2015

Posted by **m** on Saturday, July 25, 2009 at 6:39am.

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 will examine the sum of cubes of two numbers, A aand 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 non-negative integer.

A3+B3

=(A+B)(A2-AB+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

dont use this method.........

can you please answer the question in full steps, thanks

- maths -
**Jon Zhan**, Monday, August 3, 2009 at 8:46pmYou Know If Your Are trying To Solve The Whole Maths Enrichment By Yourself, You Should NOT Ask For Help On The Internet. Plus You Still Have about Two Weeks.

**Answer this Question**

**Related Questions**

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

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

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 ...

algebra - Find two consecutive positive integers such that the sum of their ...

Discrete Math - Let n be positive integer greater than 1. We call n prime if the...