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.
of positive integers with 
prime and ![\[ a^p=b!+p. \]](http://latex.artofproblemsolving.com/9/f/6/9f674dabcb364872cef4153198e2e362ae40a2fd.png)
be positive reals such that 
. Prove that ![\[18\sum_{\text{cyc}}\frac{1}{(3-c)(4-c)}+2(ab+bc+ca)\ge 15. \]](http://latex.artofproblemsolving.com/5/d/5/5d5c47a52d2d6ea7d13ce1c2fa14a08425bbfa5d.png)
Proposed by David Stoner
such that 
. Find the value of 
consisting of a prime number and two positive integers 
and 
such that 
and 
are both powers of .
board and made 
moves so that it visited all squares and returned to the starting square. At every moment, the distance from the center of the square the king was on to the center of the board was calculated. A move is called 
if this distance becomes smaller after the move. Find the maximum possible number of pleasant moves. (The chess king moves to a square adjacent either by side or by corner.)
. This is an overcount by 
. So each time we replace a human in the spot of a horse 
legs are lost. So there must be 
humans to get this down by 
. So the correct answer is 
*being sarcastic
*being sarcastic
I admit I wasn’t paying enough attention... I had meant Option B.
will be your answer
satsfying 
and:![\[ f(2n)f(2n+1)=9f(n)^2+3f(n)\]](http://latex.artofproblemsolving.com/b/c/1/bc18d6ad72589f012dcab7836228b3ed7ee061c2.png)
and let 
be reals such that 
satisfying
Prove
