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7

Part of 1981 Austrian-Polish Competition

Problems(1)

a^{2^n} - 1 has at least n + 1 distinct prime divisors

Source: Austrian Polish 1981 APMC

4/29/2020
Let a>3a > 3 be an odd integer. Show that for every positive integer nn the number a2nāˆ’1a^{2^n}- 1 has at least n+1n + 1 distinct prime divisors.
prime divisorsDivisorsnumber theory