English
Number theory
Notes on divisibility, prime numbers, congruences, and the deeper structures behind integer arithmetic. Each piece breaks down a specific theorem, identity, or technique — from Euclidean algorithm fundamentals to modular arithmetic and its applications. The focus is on clear reasoning: why things work, not just how to apply them. A place to build solid intuition for one of mathematics’ oldest and most elegant branches.
If polynomials held the Olympic Games, the undisputed champion would be this one:f(x) = x² + x + 41.
Summer, 1961. Two mathematicians — Daniel Shanks and John Wrench — launch a calculation that will go down in history.…
At first glance, prime numbers should be distributed evenly. For instance, when examining primes modulo 4, half of them should…
Mathematics seems like a science without passion. Formulas are strict, proofs are impartial. But not the story of the abc…
In ordinary arithmetic, we have the fundamental theorem of arithmetic: every integer can be factored into a product of primes…
If ancient people had calculators, they would definitely have used them to search for prime numbers. Why? Because the fascination…
Today we're talking about something fundamental: prime numbers. Primes are the basic building blocks of mathematics, yet their distribution along…
What is so hard about proving that a number can be written as a simple fraction? At first glance —…