Sum of Products of Subsets

Consider the set S={1,2,4,...,2100}S=\left\{1, 2, 4, ..., 2^{100}\right\}. There are 210112^{101}-1 non-empty subsets of this set.

For each subset AA let f(A)f(A) be the product of the elements in that subset. For example, if A={1,2,4}A=\{1, 2, 4\} then f(A)=8f(A)=8.

Find the sum of all f(A)f(A) as AA ranges over all the 210112^{101}-1 subsets. If the answer when divided by 126126 leaves a remainder of xx then find xx.

×

Problem Loading...

Note Loading...

Set Loading...