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P26 [Number Theory] - Turkish NMO 1st Round - 2004

Source:

November 15, 2013
modular arithmetic

Problem Statement

What is the last two digits of base-33 representation of 200520032004+32005^{2003^{2004}+3}?
<spanclass=′latex−bold′>(A)</span> 21<spanclass=′latex−bold′>(B)</span> 01<spanclass=′latex−bold′>(C)</span> 11<spanclass=′latex−bold′>(D)</span> 02<spanclass=′latex−bold′>(E)</span> 22 <span class='latex-bold'>(A)</span>\ 21 \qquad<span class='latex-bold'>(B)</span>\ 01 \qquad<span class='latex-bold'>(C)</span>\ 11 \qquad<span class='latex-bold'>(D)</span>\ 02 \qquad<span class='latex-bold'>(E)</span>\ 22
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