Competition problem — Number theory

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Number theory Difficulty 5.3 AIME, harder Find the answer

21. Find the least positive residues modulo 47 of
a) $2^{32}$
b) $2^{47}$
c) $2^{200}$ .

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

21. .) 42 b) 2 c) 18

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.