Tuesday, 27 September 2016

elementary number theory - Find remainder when 777777 is divided by 16


Find remainder when 777777 is divided by 16.




777=48×16+9. Then 7779(mod16).



Also by Fermat's theorem, 7771611(mod16) i.e 777151(mod16).




Also 777=51×15+4. Therefore,



777777=77751×15+4=(77715)51777411594(mod16) leading to 8181(mod16)1(mod16).



But answer given for this question is 9. Please suggest.

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