Linear Diophantine equations: a general method using extended Euclid
Solve ax + by = c without guessing: theory and example side by side, Bézout’s identity, every integer solution and non-negativity constraints. With a step-by-step laboratory.
ReadMathematics
Articles by topic
Clear, organized learning paths that build strong foundations in mathematics and computer science.
Number theory
The hundred-animal problems: a general method and 20 worked solutions
A hundred animals, a hundred coins and three prices: Diophantine equations, gcd and congruences to find every solution, or prove that none exists. Twenty problems with click-to-reveal solutions.
ReadHourglasses: 12 problems, Diophantine equations and Bézout’s identity
A collection with explained solutions: from full cycles to partly full turns, from the GCD to impossible cases. Laboratory with extended Euclid and simulation.
ReadCryptography: four methods, from Caesar to Alice and Bob
Substitution, transposition, XOR and RSA: full encryption and decryption examples with an interactive laboratory.
ReadThe Chinese remainder theorem: from Sunzi to 30 problems
Sunzi’s block method, modern congruences, and 30 interactive challenges involving coins, soldiers, calendars, and trick questions.
ReadFrom 3 and 5 to primes in arithmetic progression
Fajtlowicz’s conjecture, two ways to generate primes from 3 and 5, and a laboratory that also accepts a new starting pair.
ReadModular arithmetic: the remainders laboratory
From clocks to enormous powers: an intuitive guide to congruences with 25 problems and an interactive laboratory.
ReadThe water-jug problem: from the book’s method to step-by-step pours
Averbach and Chein’s method: interpret integer coefficients as fills and empties, construct the pours and follow them in a laboratory with two animated bars.
ReadWho occupies the billionth position?
The exact solution to a sequence-position problem in which every natural number n appears exactly n times.
ReadPrime numbers and hidden patterns
Divisibility, the sieve of Eratosthenes and regularities that help explore primes.
ReadArticles 1–10 of 10