IMO 2009 #1
by Wolstenholme, Nov 5, 2014, 9:29 PM
Let 
be a positive integer and let 
be distinct integers in the set $ \left{ 1,2,\ldots,n\right}$ such that divides 
for 
. Prove that does not divide 
Proof:
Assume the contrary, so that
for all 
(with indices taken modulo 
).
Therefore we find that
but since 
and 
are distinct elements of the set 
this is clearly impossible, contradiction!
be a positive integer and let 
be distinct integers in the set $ \left{ 1,2,\ldots,n\right}$ such that divides 
for 
. Prove that does not divide 
Proof:
Assume the contrary, so that
for all 
(with indices taken modulo 
).Therefore we find that
but since 
and 
are distinct elements of the set 
this is clearly impossible, contradiction!
August 2016
June 2016