MathDB
Help! USAMO 1991 #3

Source: USAMO 1991 #3

September 2, 2004
inductionmodular arithmeticstrong inductionnumber theoryrelatively primeprime numbersnumber theory unsolved

Problem Statement

Show that, for any fixed integer  n≥1, \,n \geq 1,\, the sequence 2, \; 2^2, \; 2^{2^2}, \; 2^{2^{2^2}}, \ldots (\mbox{mod} \; n) is eventually constant.
[The tower of exponents is defined by a1=2,  ai+1=2aia_1 = 2, \; a_{i+1} = 2^{a_i}. Also a_i \; (\mbox{mod} \; n) means the remainder which results from dividing aia_i by nn.]
Back to ProblemsView on AoPS