
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
 LinkBack  Thread Tools  Display Modes 
September 2nd, 2017, 07:19 PM  #1 
Newbie Joined: Sep 2017 From: NY Posts: 6 Thanks: 0  my problem
Hey! (x+1)^(n+1)(x1)^(n+1)=y^n There is no solutions in total numbers x, y, n. n>1 How to show it? 
September 3rd, 2017, 05:22 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,820 Thanks: 750 
"total numbers"? Do you mean "integers"?

September 3rd, 2017, 05:38 AM  #3 
Newbie Joined: Sep 2017 From: NY Posts: 6 Thanks: 0 
Yes.

October 17th, 2017, 07:47 AM  #4 
Member Joined: May 2013 Posts: 33 Thanks: 1 
look up Fermat's last theorem proof.

October 17th, 2017, 09:05 AM  #5 
Senior Member Joined: Sep 2016 From: USA Posts: 196 Thanks: 103 Math Focus: Dynamical systems, analytic function theory, numerics 
Try a simple example first. If $n=2$ then you want to prove that \[(x+1)^3  (x1)^3 = y^2 \] has no integral solutions. Suppose it did, then expanding gives us $6x^2 + 2 =y^2$. Do you see why this can't be true? Hint: compute this modulo 3. Now apply a similar idea to the general expression using the binomial theorem. 