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5Question: A geologist is analyzing a rock formation where the number of layers formed each year corresponds to the sum of the squares of the first $ n $ odd numbers. What is the remainder when this sum is divided by $ 10 $, if $ n = 7 $?
Solution: We are asked to compute the sum of the squares of the first $ 7 $ odd numbers modulo $ 10 $. The first $ 7 $ odd numbers are $ 1, 3, 5, 7, 9, 11, 13 $. Their squares are: