100 positive integers are arranged around a circle. The greatest common divisor of the numbers is 1. An allowed operation is to add to a number the greatest common divisor of its two neighbors. Show that by a sequence of such operations we can get 100 numbers, every two of which are relatively prime?
I'm a beginner so i really need your helping. Thanks a lot!
Can you help me solve this problem?
For discussing Olympiad Level Number Theory problems
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