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    Congruences : Binomial Formula and Common Factors

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    Is 5^((10^5)^(10^5)^(10^5)) congruent to 1(mod 11)? I know this answer is yes but do not know how to prove this.

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    Is 510510510 congruent to 1(mod 11)? I know this answer is yes but do not know how to prove this. ...

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