Elementary Number Theory · Number
Quadratic Residues and Reciprocity
The Law of Quadratic Reciprocity — one of Gauss’s greatest discoveries — gives a surprising relationship between solvability of x² ≡ p (mod q) and x² ≡ q (mod p).
WHAT STUDENTS WILL LEARN
✓Define quadratic residues and the Legendre symbol
✓Apply Euler’s criterion
✓State the Law of Quadratic Reciprocity
✓Solve quadratic congruences
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