Post a New Question


posted by .

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 -

    We will examine the sum of cubes of two numbers, A and B. Without losing generality, we will further assume that
    A=2nX and
    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 -

    Nice Answer, But Please Try To Use (Mod)

    That Way Is Easier

  • Maths -

    Hey, Your ANSWER is corrupt, cause it doesnt really explain anything! Try to make it more clear.


Answer This Question

First Name
School Subject
Your Answer

Related Questions

More Related Questions

Post a New Question