Difference between revisions of "2024 SSMO Team Round Problems/Problem 11"
(Created page with "==Problem== Let <math>S</math> denote the set of positive divisors of <math>5400.</math> Let <cmath>S_i = \{d \mid d \in S, \, d \equiv i \Mod4\}</cmath> and let <math>s_i</m...") |
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==Problem== | ==Problem== | ||
| − | Let <math>S</math> denote the set of positive divisors of <math>5400.</math> Let <cmath>S_i = \{d \mid d \in S, \, d \equiv i \ | + | Let <math>S</math> denote the set of positive divisors of <math>5400.</math> Let <cmath>S_i = \{d \mid d \in S, \, d \equiv i \pmod4\}</cmath> and let <math>s_i</math> denote the sum of all elements of <math>S_i.</math> Find the value of <cmath>s_0^2+s_1^2+s_2^2+s_3^2-2s_0s_2-2s_1s_3.</cmath> |
==Solution== | ==Solution== | ||
Latest revision as of 15:45, 2 May 2025
Problem
Let 
denote the set of positive divisors of 
Let ![\[S_i = \{d \mid d \in S, \, d \equiv i \pmod4\}\]](http://latex.artofproblemsolving.com/8/c/d/8cd108edc94e14f4f933e8e2b67920b2c608254c.png)
and let 
denote the sum of all elements of 
Find the value of ![\[s_0^2+s_1^2+s_2^2+s_3^2-2s_0s_2-2s_1s_3.\]](http://latex.artofproblemsolving.com/5/7/3/573a18475c4a2169e8689b1c7de50d4603a4eb70.png)
