NT6

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Find the remainder when 137153 is divided by 18.

137^{153}\equiv 11^{153}\equiv 121^{76}\times 11\equiv 13^{76}\times 11(mod18)\,

\equiv (13^3)^{25}\times 143\equiv 2197^{25}\times -1\equiv 1^{25}\times -1\equiv 17(mod18)\,


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