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So I'm not sure how bijection and modularity are related, I know that bijection is one to one and onto.

So my questions are;

Is $f(x) \equiv x^{āˆ’1} \pmod{p}$ a bijection from $\{1,...,pāˆ’1\}$ to $\{1,...,pāˆ’1\}$? And how about $f(x) = x^2 \pmod{p}$?

How do I prove these?

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whatdidthefoxsay
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  • They aren't "related"...bijection is a term given to a map of sets, but this is what you are given in the question! ā€“ fretty Sep 23 '13 at 14:45

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The first question is equivalent to asking whether all elements of $\mathbb{Z_p}$ have a unique multiplicative inverse. The answer is yes iif $p$ is prime; the inverse can be computed by the extended euclidean algorithm.

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