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last two digits of a_{1979} if a_{n+1} = 9^{a_n}

Source: Netherlands - Dutch NMO 1979 p3

January 28, 2023

recurrence relationSequencenumber theorylast digits

Problem Statement

Define

a_1 = 1979

and

a_{n+1} = 9^{a_n}

for

n = 1,2,3,...

. Determine the last two digits of

a_{1979}