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For each of the following ( mod n , either find a~ 1 mod n, i.e_ find an integer 1 with ax = 1 mod n, Or explain why such an integer does not exist:5-1 mod I1: (21)...

Question

For each of the following ( mod n , either find a~ 1 mod n, i.e_ find an integer 1 with ax = 1 mod n, Or explain why such an integer does not exist:5-1 mod I1: (21)-1 mod 28; 2-1 mod 101: 4-1 mod 101.

For each of the following ( mod n , either find a~ 1 mod n, i.e_ find an integer 1 with ax = 1 mod n, Or explain why such an integer does not exist: 5-1 mod I1: (21)-1 mod 28; 2-1 mod 101: 4-1 mod 101.



Answers

Devise a recursive algorithm for finding $x^{n}$ mod $m$ when- ever $n, x,$ and $m$ are positive integers based on the fact that $x^{n}$ mod $m=\left(x^{n-1} \bmod m \cdot x \bmod m\right) \bmod m .$


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