Number Theory and Wizards
Number Theory
Level
pending
If A={ a is the set of all natural numbers x smaller than 10000000000, such that the product of nC0, nC1, nC2..........nCn is odd}, then find the sum of all such x, in the set of A.
The answer is 17179869149.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Use Lucas theorem, to obtain the sum as summation of 2^n-1, n going from 1 to 33, hence getting (2^33-1) -33 = 2^33 - 34 = 17179869149.