2024 SSMO Team Round Problems/Problem 11

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Problem

Let $S$ denote the set of positive divisors of $5400.$ Let \[S_i = \{d \mid d \in S, \, d \equiv i \pmod4\}\] and let $s_i$ denote the sum of all elements of $S_i.$ Find the value of \[s_0^2+s_1^2+s_2^2+s_3^2-2s_0s_2-2s_1s_3.\]

Solution