What you'll learn

48 lessons in Number Theory

DivisibilityFloor, ceiling & fractional partGCD & Euclid's algorithmPrimes & unique factorizationModular arithmeticDiophantine equationsChinese Remainder TheoremEuler's totient & RSA previewQuadratic residues & reciprocityPrimitive rootsThe discrete logarithm problemContinued fractionsMultiplicative functionsSieve of Eratosthenes & sieve methodsPrime Number TheoremRiemann zeta & prime distributionElliptic curves introProof of Fermat's little theoremProof of Euclid's lemma + FTA outlineWilson's theoremCryptographic protocols (DH, RSA, ECC)Perfect numbers & Mersenne primesLegendre's formula: prime powers in n!Number bases & scales of notationThe divisor functions τ and σMultiplicative order & the group (Z/n)*Lagrange's theorem on polynomial congruencesFermat's two-square theoremLagrange's four-square theoremPell's equationFermat pseudoprimes & Carmichael numbersLifting the exponent (LTE)Gaussian integers ℤ[i]Primality testingInteger factorization algorithmsDirichlet convolution & Möbius inversionBernoulli numbers & sums of powersFarey sequences & the Stern–Brocot treeBinary quadratic forms & class numberp-adic valuation & absolute valueThe p-adic numbers ℚ_pHensel's lemmaLucas' & Kummer's theoremsThe Frobenius coin problemZsygmondy's theoremWhat $\sum_{p \le N} e^{2\pi i p\theta}$ measuresThe circle method, on one lineGoldbach, stated and placed

How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the day its model predicts you would forget it. A short placement check finds what you already know, so you start Number Theory exactly where it's useful.

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