PEN Global

Anyone who wants to contribute the PEN Global, the translation work of Problems in Elementary Number Theory 2 [ 2009 ] No. 1, please submit your translation to Yimin Ge at together with your LaTeX file, its compiled PDF file and fonts file.

You have to use the TeX file available here. Download gPENv02n1eng.tex. The deadline for your submission is 15th, July..

Before you contact Yimin Ge, please have a look at the PEN Global page at https://projectpen.wordpress.com/global .

Notice: We’ve already find translators: in Vietnamese,  Greek, Spanish, Bangla, Bosnian, Chinese, Croatian, Serbian [Latin] and Serbian [Cyrillic]

Editors-in-Chief for 2010

As you know, Problems in Elementary Number Theory 2 [ 2009 ] No. 1 is NOW online. The Editors-in-Chief of the next issue are

Daniel Kohen (Argentina)
Cosmin Pohoata (Romania)
Harun Šiljak (Bosnia and Herzegovina)
Peter Vandendriessche (Belgium)

Anyone who wants to be one of the Editors-in-Chief of the fourth and fifth issue of Problems in Elementary Number Theory (2010), APPLY NOW.

Please, send an email to us at pen@problem-solving.be with your brief C.V.

You need to know basic LaTeX skills and of course you have to be fluent with Olympiad-style problems from Elementary number theory.

We are planning to recruit two or three Editors-in-Chief for Problems in Elementary Number Theory 2010. The deadline for application is 31th, July.

from Hojoo Lee (the founder of project PEN)

Problems in Elementary Number Theory 2 [ 2009 ] No. 1

Is now available here !

This weblication is written by PEN team and contributors:

Alexander Remorov (Canada),
Darij Grinberg (Germany),
Harun Siljak (Bosnia and Herzegovina),
Marin Misur (Croatia).

We also need to thank  two Editors-in-Chief:

Daniel Kohen (Argentina) and Cosmin Pohoata (Romania).

Here goes the table of contents:

1 Problems 1

2 Articles 3

2.1 Three Ways to Attack a Functional Equation . . . . . . . . . . . . . . . . . . . . . 3

2.2 A Generalization of an Identity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Minimum prime divisors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Dierent Approaches to an Intuitive Problem . . . . . . . . . . . . . . . . . . . . . 15

2.5 Exponential Congruence Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.6 Using Quadratic Residues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.7 A Hidden Divisibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.8 Fractions Mod p and Wolstenholme’s theorem . . . . . . . . . . . . . . . . . . . . . 29

2.9 A binomial sum divisible by primes . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.10 Sequences of Consecutive Integers . . . . . .

1 Problems 1

2 Articles 3

2.1 Three Ways to Attack a Functional Equation . . . . . . . . . . . . . . . . . . . . . 3

2.2 A Generalization of an Identity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Minimum prime divisors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Dierent Approaches to an Intuitive Problem . . . . . . . . . . . . . . . . . . . . . 15

2.5 Exponential Congruence Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.6 Using Quadratic Residues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.7 A Hidden Divisibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.8 Fractions Mod p and Wolstenholme’s theorem . . . . . . . . . . . . . . . . . . . . . 29

2.9 A binomial sum divisible by primes . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.10 Sequences of Consecutive Integers . . . . . .