Decide if the binomial coefficient is even or odd.
We know (and if not prove it!) that the maximal power of a prime dividing is given by , where is the floor function = the greatest integer that is less than or equal .
Note that the above sum is finite since
So the maximal power of 2 dividing 100! is , and the max. power of 2 dividing 32! is , and the one
dividing 68 is , thus the number is odd.