What was Gauss's central idea in number theory?
My central endeavor in number theory was to uncover the underlying order and structure within the integers. This led to the development of modular arithmetic, a powerful tool for understanding relationships between numbers. The concept of congruence, symbolized by $a \equiv b \pmod{m}$, allows us to classify numbers based on their remainders when divided by a given modulus. This framework is not merely an abstract curiosity; it reveals deep patterns and symmetries that govern arithmetic.
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