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.
be reals such that 
Show that
Let 
and Show that
distinct divisors of a positive integer number 
form an arithmetic progression. Prove that the number has at least 
divisors.
be distinct real numbers such that 
Find the value of 
be distinct real numbers such that 
Find the value of 
be distinct real numbers such that 
Find the value of 
![\[222{,}222-22{,}222-2{,}222-222-22-2?\]](http://latex.artofproblemsolving.com/1/5/6/156c3662fe4c874a80e54887f76c302c13b9d14c.png)
are multiples of 
or 
but not 
?
, let![\[a_n = \frac {(n + 9)!}{(n - 1)!}.\]](http://latex.artofproblemsolving.com/f/d/5/fd5a5ee0252b440fd5fcd9694ac0b00de61b83b2.png)
denote the smallest positive integer for which the rightmost nonzero digit of 
is odd. The rightmost nonzero digit of is
and 
.
satisfy that: 
.
and 
Find the value range of 
