Final answer:
The number of distinct triplets of stock costs that sum up to a number divisible by d is determined using Modular arithmetic and Combinatorial analysis to categorize and count the occurrences of remainders when divided by d, then calculating combinations that satisfy the divisibility condition.
Step-by-step explanation:
The question revolves around the use of Modular arithmetic to determine the number of distinct triplets of stock costs that sum up to a number divisible by a given integer d. To find a solution to this problem, we can follow a combinatorial analysis approach but using concepts of modular arithmetic. In particular, we'd want to count all possible triplets (i.e., groups of three) from the array of stock costs in which the sum of the triplet members is divisible by d.
To achieve this, we first calculate the remainder of each stock cost when divided by d (using modular arithmetic). Next, we categorize these remainders and count the number of times each remainder occurs. With these counts, we can then determine the number of triplets that add up to a multiple of d by selecting triplets that, once their remainders are added together, result in a sum that is divisible by d.
This involves combinatorial calculations, as we are essentially choosing sets of three from the array that fulfill our divisible by d criterion. However, there's no requirement for cubing numbers (no need for the cubic root) or using prime factorization. Therefore, the subject of this question is best described by Modular arithmetic and Combinatorial analysis.