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Home » So, \( 2^x+1 = 2^5 \). - Blask

So, \( 2^x+1 = 2^5 \). - Blask

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 So \( a = 5b + 1 \), then \( N = 4(5b + 1) + 3 = 20b + 7 \)

📌 Thus, \( N \equiv 7 \pmod{20} \)

📌 Step 2: Incorporate \( N \equiv 4 \pmod{7} \)

📌 Let \( N = 20b + 7 \). Then:

📌 20b + 7 \equiv 4 \pmod{7} \Rightarrow 20b \equiv -3 \equiv 4 \pmod{7}

📌 Since \( 20 \equiv 6 \equiv -1 \pmod{7} \), we have:

📌 b \equiv 4 \pmod{7} \Rightarrow b \equiv -4 \equiv 3 \pmod{7}

📌 So \( b = 7c + 3 \), then:

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