2. Let p and p²+2 be prime nubers. Proove, that number p³+2 is prime number.

3. Sequence {p_n}_n=1^oo is recursive defined: p₁ = 2 , and for n N, n > 1 is p_n the biggest prime number divisor of number p₁. p₂. p₃. ... . p_n-1+1. Proove, that any member of this sequence is not equal to 5.

4. Proove, that if p is prime number and n is natural number (n p), then number

n p

-

n p

is divisible by p ([x] means integer part of real number x).

5. Fraction q/p, where p 5 is odd prime number, is written as decimal number. Proove, that number of digits in the shortest period is even, only when their aritmetic average is equal to 9/2.

Problems in this series has been chosen by Eno Kovac (1, 2), Juro Foldes (3, 4, 5) and translated by Koli

The deadline for sending the solutions is 30th november 1998.

Send your solutions to the following address:

	BKMS
RNDr.	Jaroslav Gurican, CSc.
	KATC
	MFF UK
	Mlynska dolina
842 15	Bratislava
	Slovak Republic

Or you may try send me solutions by e-mail in AmS-TEX format.

Solution of each problem has to be on the separate sheet of paper. Don't forget to include your name, address, school and age.