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 a prime such that: 
. Simplify:
be a given integer. The Mint issues coins of 
different values 
, where each 
is a positive integer (the number of coins of each value is unlimited). A set of values 
is called lucky, if the sum 
can be collected in a unique way (namely, by taking one coin of each value).
with 
(b) Prove that every lucky set of values satisfies 
is a given prime number.
is a set which 
.
non-empty subsets 
of 
such that 
can be written in the form
where 
are non negative integers, such that
for every 
.
Prove that
Where 
Prove that
be real numbers such that 
. Find the smallest possible value of 
.
with the property that for every real numbers 
and 
it holds that
along the perimeter of a circle, then every word of the length 
consisting of letters and (i.e. 
, 
, 
, 
, 
, 
, 
, 
) occurs exactly once on the perimeter. Decide whether it is possible to write a sequence of letters from a 
-element alphabet along the perimeter of a circle in such a way that every word of the length 
(i.e. an ordered -tuple of letters) occurs exactly once on the perimeter.
and 
.
