A 1007th degree equation

Number Theory Level 2

( n − 1 ) ( n − 3 ) ( n − 5 ) ⋯ ( n − 2013 ) = n ( n + 2 ) ( n + 4 ) ⋯ ( n + 2012 ) (n -1)(n - 3)(n - 5) \cdots (n -2013) = n(n + 2)(n + 4) \cdots(n + 2012)

How many integer solutions are there for the equation above?


The answer is 0.

View wiki
Math Man by math man , 20, Indonesia

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Ronald Overwater
Apr 8, 2015

If n is odd, the LHS is even or zero and the RHS is odd.

If n is even, the LHS is odd and the RHS is even or zero.

So there is no integer solution for the equation.

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

It is just that simple. Well done!

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...