Recruiting is finally over. We now have 10 members:
Andrei Frimu (Moldova)
Yimin Ge (Austria)
Ofir Gorodetsky (Israel)
Daniel Kohen (Argentina)
David Kotik (Canada)
Hojoo Lee (Korea)
Soo-Hong Lee (Korea)
Cosmin Pohoata (Romania)
Ho Chung Siu (Hong Kong)
Peter Vandendriessche (Belgium)
As you see, the current version of PEN extended does not contain the problems in year 2008.
Please, send us number theory problems in national math olympiads ( taken in between September ‘07 and June ‘08 ) and selection test for IMO 2008 from your country. The problems we receive will be included in the first edition of PEN extended with contributor’s name. The TeX format is available HERE.
from PEN TEAM
Before submitting your TeX file, check out the following list. The national codes are from http://www.imo-official.org
To PEN friends.
After about two months, we will weblish the first official edition of PEN extended with more problems. This means that PEN Problems Book has at least 1000 challenging Problems in Elementary Number theory.
THE NEXT STEP IS OBVIOUS: THE EFFICIENT USE OF DATABASE. It entirely depends on you, PEN friends! To complete PEN Solutions Book, we need your help and more PEN Team members.
We all wait your creative solutions(including generalizations and comments) for problems in PEN Problems Book or in PEN extended. We want young minds who proofread “with sharp eyes” the solutions in our supporting site at ML. We need more people who do the TeXing work on the PEN Problems Book. If you want to participate this forever Project, then please let us know!
The second season of Problems of Bi-Week Project will begin later, not starting in 1st July. At least after IMO, maybe around August. All I can say now is that it will take some time. I hope, at least before the second week of September. In the second season, we will meet many number theory problems from IMO Short List Book ‘07. See you soon!
from PEN Team
Hi, PEN FRIENDS!
Here is the pdf file of PEN extended (version 0.9)! Lots of interesting problems from recent mathematics olympiads are available, YAY! Good problems from this book will be taken, and included to the original PEN Problems Book. If you find any typos or errors, then please email us at pen@problem-solving.be
PEN Problems Book has 649 problems and PEN extended has 337 problems!
- PEN TEAM
One more thing. We have a Project PEN Group on facebook. Anyone who loves number theory is welcome!
Hi, all! Now, we have a summer break. The second season of PEN will begin in July!
10. PEN B6 Consider the set of all five-digit numbers whose decimal representation is a permutation of the digits 
. Prove that this set can be divided into two groups, in such a way that the sum of the squares of the numbers in each group is the same.
Here is the official solution file: PEN10S
You can also disscuss the problems here!
10. PEN B6 Consider the set of all five-digit numbers whose decimal representation is a permutation of the digits . Prove that this set can be divided into two groups, in such a way that the sum of the squares of the numbers in each group is the same.
does not have a primitive root. Show that
relatively prime to 
be a prime number and 
be integers.
is an arithmetic progression if and only if there exists a partition of 
into sets 
such that
denotes the set 
.