MathDB
TOT 1998 Spring AS3 1,2, 22,23 ,..., 210 written on blackboard.

Source:

May 11, 2020
combinatorics

Problem Statement

(a) The numbers 1,2,4,8,16,32,64,1281 , 2, 4, 8, 1 6 , 32, 64, 1 28 are written on a blackboard. We are allowed to erase any two numbers and write their difference instead (this is always a non-negative number). After this procedure has been repeated seven times, only a single number will remain. Could this number be 9797? (b) The numbers 1,2,22,23,...,2101 , 2, 22, 23 , . . . , 210 are written on a blackboard. We are allowed to erase any two numbers and write their difference instead (this is always a non-negative number) . After this procedure has been repeated ten times, only a single number will remain. What values could this number have?
(A.Shapovalov)
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