maths

posted by .

can you answer this question:
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 and 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 -

    You 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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. discrete math

    1)prove that if x is rational and x not equal to 0, then 1/x is rational. 2) prove that there is a positive integers that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive?
  2. math, algebra

    2a+2ab+2b I need a lot of help in this one. it says find two consecutive positive integers such that the sum of their square is 85. how would i do this one i have no clue i know what are positive integers.but i don't know how to figure …
  3. algebra

    The positive integer 4 can be represented as a sum of 1's or 2's in five ways, such as 1 + 2 + 1 and 1 + 1 + 2. Show all the ways that the positive integer 5 can be represented as a sum of 1's or 2's.
  4. Maths

    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. thanx
  5. math

    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. thanx
  6. math

    can you answer this question in a different and more logical way than this method below: we will examine the sum of cubes of two numbers, A and B. Without losing generality, we will further assume that A=2nX and B=2n+kY where X is …
  7. MATH

    Find the only positive integer whose cube is the sum of the cubes of three positive integers immediately preceding it. Find this positive integer. Your algebraic work must be detailed enough to show this is the only positive integer …
  8. math

    Which statement is true? A.The sum of two positive integers is sometimes positive, sometimes negative. B.The sum of two negative integers is always negative. C.The sum of a positive integer and a negative integer is always positive.
  9. math

    Find the sum of the first one thousand positive integers. Explain how you arrived at your result. Now explain how to find the sum of the first n positive integers, where n is any positive integer, without adding a long list of positive …
  10. maths

    the non- decreasing sequence of odd integers {a1, a2, a3, . . .} = {1,3,3,3,5,5,5,5,5,...} each positive odd integer k appears k times. it is a fact that there are integers b, c, and d such that, for all positive integers n, añ = …

More Similar Questions