Posted by Matt on Wednesday, July 15, 2009 at 11:27pm.
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.
- Maths - MathMate, Thursday, July 16, 2009 at 6:38am
We will examine the sum of cubes of two numbers, A aand B. Without losing generality, we will further assume that
X is not divisible by 2
n is a positive integer and
k is a non-negative integer.
=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
- Maths - Jon Zhan, Monday, August 3, 2009 at 8:47pm
Nice Answer, But Please Try To Use (Mod)
That Way Is Easier
- Maths - Sean, Monday, August 17, 2009 at 6:01am
Hey, Your ANSWER is corrupt, cause it doesnt really explain anything! Try to make it more clear.
Answer This Question
More 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 ...
- MATH - Find the only positive integer whose cube is the sum of the cubes of ...
- discrete math - 1)prove that if x is rational and x not equal to 0, then 1/x is ...
- 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 ...