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  • https://math.libretexts.org/Courses/Las_Positas_College/Math_for_Liberal_Arts/05%3A_Numeration_Systems/5.04%3A_Modular_Systems
    In terms of division, we say that a divides b if and only if the remainder is zero when b is divided by a. In the late third century, the Chinese mathematician Sun Tzu asked his studen...In terms of division, we say that a divides b if and only if the remainder is zero when b is divided by a. In the late third century, the Chinese mathematician Sun Tzu asked his students: "We have things of which we do not know the number; if we count by threes, the remainder is 2; if we count be fives, the remainder is 3; if we count by sevens, the remainder is 2.
  • https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/A_Spiral_Workbook_for_Discrete_Mathematics_(Kwong)/05%3A_Basic_Number_Theory/5.07%3A_Modular_Arithmetic
    The notation “(mod n)” after m_1\equiv m_2 indicates a congruence relation, in which “mod n” are enclosed by a pair of parentheses, and the notation is placed at the end of the congruence....The notation “(mod n)” after m_1\equiv m_2 indicates a congruence relation, in which “mod n” are enclosed by a pair of parentheses, and the notation is placed at the end of the congruence. Given any integer m, m\bmod n \in\{0,1,2,\ldots,n-1\}. \nonumber We call these values the residues modulo . In modular arithmetic, when we say “reduced modulo ,” we mean whatever result we obtain, we divide it by n, and report only the smallest possible nonnegative residue.

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