Problem Set 1
Euclid and the architecture of the integers
Divisibility, greatest common divisors, Bézout identities, prime factorization, and the infinitude of primes.
10 problems
and Primes
Number theory · Student editions
Problem sets
& quizzes.
A place to practice, put a proof together, and check what you understand. Download a handout and make the work your own.
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Develop the argument
Problem sets
Week 2
Division, primes, and finite continued fractions
Turn Euclidean calculations, a sieve, and finite continued fractions into proofs. Test divisibility claims with counterexamples.
8 core problems + challenge · 2–3 hours
Problem Set 3
Totients, divisor sums, and exact periods
Extended Euclid and Euler's theorem lead into multiplicative functions, Möbius inversion, necklace counts, and squarefree integers.
8 problems + challenge · 100 points · 3–4 hours
Problem Set 4 · Optional enrichment
Orders, interpolation, and Fourier inversion
Invert counts on posets, subsets, and partitions, then recover polynomial coefficients at roots of unity and explore cyclic convolution.
6 problems + challenge · 80 points · 3–4 hours
Check your understanding
Quizzes
Weekly quiz collection
Ten checkpoints from Euclid to primes
Short, self-contained quizzes following the course sequence, with space to write calculations and proofs.
10 quizzes · 20 minutes each · 10 points each