Unclassified Questions

2021 GMC 10B Problems/Problem 19

Find the remainder when is divided by .

2293^{18}-1=(3^6\cdot3^6\cdot3^6)-1$$ (Error compiling LaTeX. Unknown error_msg)\qquad\qquad =(729\cdot729\cdot729)-1$$ (Error compiling LaTeX. Unknown error_msg)\qquad\qquad\equiv (-82\cdot-82\cdot-82)-1\mod811$$ (Error compiling LaTeX. Unknown error_msg)\qquad\qquad\equiv -(2^3)(41^3)-1\mod811$$ (Error compiling LaTeX. Unknown error_msg)\qquad\qquad\equiv -(8)(41)(41^2)-1\mod811$$ (Error compiling LaTeX. Unknown error_msg)\qquad\qquad\equiv -(328)(1681)-1\mod811$$ (Error compiling LaTeX. Unknown error_msg)\qquad\qquad\equiv -(-483)(59)-1\mod811$$ (Error compiling LaTeX. Unknown error_msg)\qquad\qquad\equiv 28496\mod811$$ (Error compiling LaTeX. Unknown error_msg)\qquad\qquad\equiv 111\mod811$