Can you help me solve this problem?

For discussing Olympiad Level Number Theory problems
admin859213
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Can you help me solve this problem?

Unread post by admin859213 » Sun Dec 30, 2018 12:08 pm

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!

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