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Home » Step 2: Compute initial terms numerically - Get link 4share

Step 2: Compute initial terms numerically - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 $ 45 \equiv 1 \pmod{4} $ (since $ 44 = 11 \cdot 4 $)

📌 So the divisors $ \equiv 1 \pmod{4} $ are: $ 1, 5, 9, 45 $.

📌 + 5 + 9 + 45 = 60

📌 Thus, the sum of all positive divisors of $ 1440 $ congruent to $ 1 \pmod{4} $ is $ \boxed{60} $.

📌 Question: What is the remainder when $ 1001 + 1003 + 1005 + \cdots + 1099 $ is divided by $ 16 $?

📌 Solution: The sequence is an arithmetic series of odd numbers from 1001 to 1099, inclusive.

📌 First, find the number of terms. This is an arithmetic sequence with:

📌 First term $ a = 1001 $

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