Remainders & Modular Arithmetic

When division repeats in fixed groups, only the leftover position matters; numbers with the same remainder therefore behave alike for many purposes.

What you'll learn

  • Write division as n = dq + r with 0 ≤ r < d.
  • Group integers into remainder classes and recognize that differences within a class are multiples of the modulus.
  • Interpret congruence as same remainder rather than ordinary equality.
  • Combine and filter remainder conditions while retaining the required final remainder.

Before you start

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