Problem

Source: Iranian National Olympiad (3rd Round) 2008

Tags: inequalities, number theory proposed, number theory



In an old script found in ruins of Perspolis is written: This script has been finished in a year whose 13th power is 258145266804692077858261512663 You should know that if you are skilled in Arithmetics you will know the year this script is finished easily. Find the year the script is finished. Give a reason for your answer.