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.
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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.
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.
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