Prove $2^{1092}\equiv 1 \pmod {1093^2}$, and $3^{1092} \not \equiv 1 \pmod {1093^2}$

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I did try to factorise 1092 and it is equal to $2^2*3*7*13$ and I really don't know what I can do with this. Do I need to calculate all the powers?

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Here is the demonstration for $2^{1092}\equiv 1 \pmod {1093^2}$

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