Art of Problem Solving Wiki
Art of Problem Solving
Art of Problem Solving wiki entry on quadratic residues, defining them modulo n, introducing the Legendre symbol and Euler's criterion, and showing how residues are used in olympiad-style number theory problems. Good for competition-oriented learners building modular arithmetic skills.
More resources on Quadratic Residues
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Brilliant.org
Brilliant's wiki page on quadratic residues, covering the definition, Euler's criterion, the Legendre symbol, and quadratic reciprocity, with worked problems. Readers learn to decide whether an integer is a square modulo a prime.
Number Theory
Four-week UC San Diego course building from division with remainder and modular arithmetic to Euclid's algorithm and RSA. Finishing it, you can encrypt and decrypt messages and break RSA implementations that reuse or mishandle keys.
A Course in Number Theory and Cryptography
Graduate Texts in Mathematics volume introducing elementary number theory alongside its cryptographic applications: finite fields, quadratic residues and reciprocity, public-key cryptosystems, primality testing, factoring, and elliptic curves. Readers learn the mathematics behind RSA and elliptic-curve cryptography.