  A determined algorithm is presented for solving the rSUM problem for any
natural r with a sub-quadratic assessment of time complexity in some cases. In
terms of an amount of memory used the obtained algorithm is the nlog^3(n)
order.
  The idea of the obtained algorithm is based not considering integer numbers,
but rather k (is a natural) successive bits of these numbers in the binary
numeration system. It is shown that if a sum of integer numbers is equal to
zero, then the sum of numbers presented by any k successive bits of these
numbers must be sufficiently "close" to zero. This makes it possible to discard
the numbers, which a fortiori, do not establish the solution.
