## What is a Solution to an Equation?

How to Write the Solution: Call the 100 integers n_1, n_2, \ldots, n_ {100} . Let S_k = n_1 + n_2 + \dots + n_k for k = 1, 2, \dots, 100. Case 1: If S_1, S_2,\dots, S_ {100} are all distinct (mod