MathNumber theory

Modulo division with negative numbers

Signs

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Suppose that the dividend aa is a negative integer and the divisor dd is a positive integer.

Let's denote by qEq_E and rEr_E the quotient and the remainder in Euclidean division, by qFq_F and rFr_F - the quotient and the remainder in Floored division, by qTq_T and rTr_T - the quotient and the remainder in Truncated division.

What we can say about the signs of qE,rE,qF,rF,qTq_E, r_E, q_F, r_F, q_T, and rTr_T? Choose all correct statements.

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