Matching sums of consecutive elements of two sets

Question

Given two sets of integers P and C of the same length. How can I find ALL matching sums of consecutive elements at the same starting and ending positions in the two sets, including overlapping subsets?

C# is preferred but non-Linq please.

Example:

Let P and C be the sets of the first ten prime and composite numbers:
P = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 }
C = { 4, 6, 8, 9, 10, 12, 14, 15, 16, 18 }

Match 1: [index starts at 0]
SumP[3..5] = 7 + 11 + 13 = 31
SumC[3..5] = 9 + 10 + 12 = 31

Match 2: [index starts at 0]
SumP[2, 6] = 5 + 7 + 11 + 13 + 17 = 53
SumC[2, 6] = 8 + 9 + 10 + 12 + 14 = 53

I need to find if the above two sums are the only ones or not!

Answer 1

Here's the brute force approach with nested for loops, ignoring the "overlapping" part which I don't understand yet:

for(int indexA=0; indexA<P.Length; indexA++) {
  for(int indexB=indexA; indexB<P.Length; indexB++) {
    int sumA = 0, sumB = 0;
    for(int i=indexA; i<=indexB; i++) {
      sumA += P[i];
      sumB += C[i];
    }
    if (sumA == sumB) {
      Console.WriteLine("[" + indexA + ", " + indexB + "] : Sum = " + sumA);
    }
  }
}

Output:

[2, 6] : Sum = 53
[3, 5] : Sum = 31