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last 2 digits 2^5 + 2^{5^2}} + 2^{5^{3}} +... + 2^{5^{1991}}

Source: Nordic Mathematical Contest 1991 #1

October 5, 2017

Last digitnumber theory

Problem Statement

Determine the last two digits of the number

2^5 + 2^{5^{2}} + 2^{5^{3}} +... + 2^{5^{1991}}

, written in decimal notation.