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The Java Language Specification (JLS) [JLS 2011], §15.17.3, "Remainder Operator %,", states

The remainder operation for operands that are integers after binary numeric promotion (§5.6.2) 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.

The result of the remainder operator has the same sign as the dividend (the first operand in the expression).:

5 % 3 produces 2
5 % (-3) produces 2
(-5) % 3 produces -2
(-5) % (-3) produces -2

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This compliant solution calls the imod() method that always returns a positive remainder.:

// method imod() gives non-negativenonnegative result
private int SIZE = 16;
public int[] hash = new int[SIZE];

private int imod(int i, int j) {
  int temp = i % j;
  return (temp < 0) ? -temp : temp; // unaryUnary - will succeed without overflow  
                                    // because temp cannot be Integer.MIN_VALUE
}
	
public int lookup(int hashKey) {
  return hash[imod(hashKey, SIZE)];
}

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