📂Number Theory

Quotient and Remainder

Definition ¹

Given two integers $A$ and $B \ne 0$, suppose there exist integers $Q$ and $R$ that satisfy $$ A = Q \cdot B + R $$ . In this case, $Q$ is called the Quotient, and $R$ is called the Remainder.

Explanation

I’m not sure how quotients and remainders are defined in elementary schools these days, but there might be differences from the strict levels of discrete mathematics and number theory. Notably, the definition does not describe the quotient and remainder as results of division, but rather as means of expressing integers. This might seem trivial, but it represents a shift in mathematical interest from techniques and methods of calculation to exploration of abstract entities.