1

Part of 2010 International Zhautykov Olympiad

Problems(2)

CNT from IZhO 2010 2-nd round-1

Source:

Positive integers

1,2,...,n

are written on а blackboard (

n >2

). Every minute two numbers are erased and the least prime divisor of their sum is written. In the end only the number 97 remains. Find the least

n

for which it is possible.

combinatorics proposedcombinatorics

IZhO 2010 1-st round-1

Source:

Find all primes

p,q

p^3-q^7=p-q

number theory proposednumber theory