09. PEN B6 Suppose that does not have a primitive root. Show that

for every relatively prime to .

Here is the official solution file: pen09.

You can also disscuss the problems here!

Posted in PEN Solutions Archive on April 30, 2008| Leave a Comment »

Posted in Problem of the Bi-Week on April 23, 2008| Leave a Comment »

09. PEN B6 Suppose that does not have a primitive root. Show that

for every relatively prime to .

Posted in PEN Solutions Archive on April 17, 2008| Leave a Comment »

Posted in Problem of the Bi-Week on April 9, 2008| Leave a Comment »

08. PEN O 35 ( Romania TST 1998 )

Let be a prime number and be integers.

Prove that is an arithmetic progression if and only if there exists a partition of into sets such that

where denotes the set .

Posted in PEN Solutions Archive on April 2, 2008| Leave a Comment »