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Algebra-ish problem

Source: Russian TST 2014, Day 10 P1 (Groups A & B) [thank you for the translation, Phorphyrion]

January 8, 2024
algebra

Problem Statement

Nine numbers a,b,c,…a, b, c, \dots are arranged around a circle. All numbers of the form a+bc,…a+b^c, \dots are prime. What is the largest possible number of different numbers among a,b,c,…a, b, c, \dots?
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