Math & Bit Manipulation

Keep replacing the pair with the smaller number and the remainder until the remainder is zero; the last non-zero number is the GCD.

Expected sum minus actual sum gives the missing number, or XOR everything so present numbers cancel and only the missing one remains.

Place each value v at index v, then the first index where index != value is the missing number.

Place v at index v-1; every slot where value != index+1 is a missing number.

Make an all-ones mask as wide as the number, then XOR to flip only the bits the number uses.

XOR with one inverts a bit, so reverse each row from both ends while XOR-ing each value with one in a single pass.