Quadratic residue

A quadratic residue (mod p) refers to an integer c such that there exists an integer x for which the congruence $$ x^2 \equiv c (mod  p)$$ holds, right?
$$x^2(mod  p) \equiv c (mod  p)$$
Which means that remainder of x^2 divided by p is the same as remainder of c divided by p.

Why c is called a residue? Residue of what?


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Kav10 Kav10
  • But in the case when c > p, it can’t be called residue since it is not, it will leave some residue, but it itself is not, right?

    • Kav10 Kav10

      That is correct. It will create the residue if you do one more mod as shown in the example.

The answer is accepted.
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