Combining two consecutive integers starting with an even one yields one. xxxxxxx0 ^ xxxxxxx1 = 00000001 If we start at a number divisible by four and do th

Combining two consecutive integers starting with an even one yields one. xxxxxxx0 ^ xxxxxxx1 = 00000001 If we start at a number divisible by four and do this twice, we get one twice. xxxxxx00 ^ xxxxxx01 = 00000001 xxxxxx10 ^ xxxxxx11 = 00000001 And combining the two of course yields zero and we are right back at the start.