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.
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