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Home » But each \((m,n)\) is distinct, so 16 solutions. - jntua results

But each \((m,n)\) is distinct, so 16 solutions. - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 S = \frac{n}{2}(a + l) = \frac{50}{2}(1001 + 1099) = 25 \cdot 2100 = 52500

📌 Now compute $ 52500 \mod 16 $.

📌 Note that $ 16 = 2^4 $. We can compute $ 52500 \div 16 $, or use modular arithmetic:

📌 First, $ 1000 \equiv 8 \pmod{16} $, so $ 5000 = 5 \cdot 1000 \equiv 5 \cdot 8 = 40 \equiv 8 \pmod{16} $ (since $ 40 - 2 \cdot 16 = 8 $)

📌 Then $ 52500 = 5000 + 500 = 8 + 500 $

📌 Now $ 500 \div 16 $: $ 16 \cdot 31 = 496 $, so $ 500 \equiv 4 \pmod{16} $

📌 Thus $ 52500 \equiv 8 + 4 = 12 \pmod{16} $

📌 Alternatively, divide directly:

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Thus, the formula becomes $ T = r^{3/2} $.
Now substitute $ r = 9 $:
T = 9^{3/2} = (9^{1/2})^3 = 3^3 = 27
oxed{27}
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