zkcalen5082 zkcalen5082

04-07-2019
Mathematics

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Find the remainder when dividing 2^2013 by 15.

Answer should be in modulo. Example: Find the remainder when dividing 2^100 by 21 and the answer is 2^100 = 16mod(21).

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konrad509 konrad509

04-07-2019

[tex]2^{2013}=2^{4\cdot503+1}\\\\2^4=16\equiv 1\pmod{15}\\2^{4\cdot 503}\equiv 1\pmod{15}\\2^{4\cdot 503+1}\equiv 2\pmod{15}\\\\2^{2013}\equiv 2\pmod{15}[/tex]

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