  The problem PosSLP is the problem of determining whether a given
straight-line program (SLP) computes a positive integer. PosSLP was introduced
by Allender et al. to study the complexity of numerical analysis (Allender et
al., 2009). PosSLP can also be reformulated as the problem of deciding whether
the integer computed by a given SLP can be expressed as the sum of squares of
four integers, based on the well-known result by Lagrange in 1770, which
demonstrated that every natural number can be represented as the sum of four
non-negative integer squares.
  In this paper, we explore several natural extensions of this problem by
investigating whether the positive integer computed by a given SLP can be
written as the sum of squares of two or three integers. We delve into the
complexity of these variations and demonstrate relations between the complexity
of the original PosSLP problem and the complexity of these related problems.
Additionally, we introduce a new intriguing problem called Div2SLP and
illustrate how Div2SLP is connected to DegSLP and the problem of whether an SLP
computes an integer expressible as the sum of three squares.
  By comprehending the connections between these problems, our results offer a
deeper understanding of decision problems associated with SLPs and open avenues
for further exciting research
