NT6

From Example Problems
Jump to: navigation, search

Find the remainder when 137^{{153}} is divided by 18.

137^{{153}}\equiv 11^{{153}}\equiv 121^{{76}}\times 11\equiv 13^{{76}}\times 11({\mathrm  {mod}}18)\,

\equiv (13^{3})^{{25}}\times 143\equiv 2197^{{25}}\times -1\equiv 1^{{25}}\times -1\equiv 17({\mathrm  {mod}}18)\,


Main Page : Number Theory