why is 4 -8 equal to 4?

This is covered in detail in the Java language specification section 15.17.3.

The remainder operation for operands that are integers after binary numeric promotion (ยง5.6) produces a result value such that (a/b)*b+(a%b) is equal to a.

This identity holds even in the special case that the dividend is the negative integer of largest possible magnitude for its type and the divisor is -1 (the remainder is 0).

It follows from this rule that the result of the remainder operation can be negative only if the dividend is negative, and can be positive only if the dividend is positive. Moreover, the magnitude of the result is always less than the magnitude of the divisor.

So, for example, -4 % 8 is indeed -4, but since 4/-8 is 0, and 0 * -8 == 0, the remainder 4 % -8 has to be 4.

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