posted by Matt on .
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.
We will examine the sum of cubes of two numbers, A and 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
Nice Answer, But Please Try To Use (Mod)
That Way Is Easier
Hey, Your ANSWER is corrupt, cause it doesnt really explain anything! Try to make it more clear.