Divisibility and Prime Numbers
Number theory explores properties of integers, including primality, divisibility, and congruences, crucial in cryptography and coding theory.
a ≡ b (mod n)
Diophantine Equations
Number theory provides tools for solving equations involving integers, essential in computer science, algebra, and geometry.
ax + by = c
Congruences and Modular Forms
Number theory has far-reaching implications in mathematics, physics, and engineering, including elliptic curves and modular forms.
f(z) = ∑[a_n e^(2πinz)]