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Home » 10 Ultimate Train Clipart Graphics You Can’t Stop Using—Free Download! - Baxtercollege

10 Ultimate Train Clipart Graphics You Can’t Stop Using—Free Download! - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 $ 15 \equiv 3 \pmod{4} $

📌 $ 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:

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Subtract \( 0.3x \) from both sides:
\[ 0.5 = 0.1x + 0.2 \]
Subtract 0.2 from both sides:
\[ 0.3 = 0.1x \]
Divide both sides by 0.1:
\[ x = 3 \]
Thus, the value of \( x \) such that \( f_A = f_B \) is:
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