Python modulo negative numbers

Question

9%2=1
9%3=0
3%9=3
how about
-9%3
-3%9
9%-3
3%-9
-9%-3
-3%-9
-9%-9
-9%9
9%-9
is there any formula to calculate this?

Answer 1

thank you for the explanation

Answer 2

One more thing, why 9%-4 is -3 but not 1

Answer 3

There are two conventions, depending on whether you allow the remainder to be negative:
−17 = −5 * 3 + −2
or not:
−17 = −6 * 3 + 1

Python's modulo operator always return a remainder that has the same sign as the denominator:

-9%3 = 0 -> no remainder
-3%9 = 6 -> -3 = -1 * 9 + 6
9%-3 = 0 -> no remainder
3%-9 = -6 -> 3 = -1 * -9 + -6
-9%-3 = 0 -> no remainder
-3%-9 = -3 -> -3 = 0 * -9 + -3
-9%-9 = 0 -> no remainder
-9%9 = 0 -> no remainder
9%-9 = 0 -> no remainder

Answer 4

ok thank you guys

Answer 5

This was really complicated🙈, thank you for such a simple explanation