AoPS Academy
[/quote]
, do not answer with "
is a solution" only. Either you post any kind of proof or at least something unexpected (like "
is the smallest solution). Someone that does not see that is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Prove that
Where 
Prove that
be complex numbers such that 
and 
.
be positive real numbers such that 
and 
, prove that
is defined below. 
Show that for all nonnegative integer 
, 
is a positive integer.
![\[\frac {x^{7} - 1}{x - 1} = y^{5} - 1.\]](http://latex.artofproblemsolving.com/7/6/2/762492979b016e0f573b993b67a2b26dfb8888f4.png)
Prove that
Where 
Prove that
Let 
Prove that
+2 w
with 
, point 
lies strictly between 
and 
on side 
, and point 
lies strictly between and 
on side 
such that 
. The degree measure of 
is 
, where 
and are relatively prime positive integers. Find 
.
but ham not getting one thing that what's the motivation is it like previously determined which inequality we have to come up with then use gcd or we use gcd to go to that inequality .I searched for this on MSE also but got nothing
be a prime such that: 
.
