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Home » Twin vs Full: Why Most Get This Terminology WRONG – Discover the Secret! - Sterling Industries

Twin vs Full: Why Most Get This Terminology WRONG – Discover the Secret! - Sterling Industries

📅 April 17, 2026 👤 scraface

Apr 17, 2026

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📌 4k \equiv 3 \pmod{5} \implies k \equiv 2 \pmod{5} \quad \text{(since } 4^{-1} \equiv 4 \pmod{5}, \text{ so } k \equiv 4 \cdot 3 = 12 \equiv 2 \pmod{5})

📌 Thus, \( k = 5m + 2 \), so \( n = 10(5m + 2) + 4 = 50m + 24 \). The smallest positive \( n \) is \( n = 24 \). Check: \( 24^2 = 576 \), ends in 76 — valid.

📌 Now consider \( n \equiv 6 \pmod{10} \): \( n = 10k + 6 \).

📌 n^2 = 100k^2 + 120k + 36 \equiv 20k + 36 \pmod{100}

📌 Set \( 20k + 36 \equiv 76 \pmod{100} \):

📌 20k \equiv 40 \pmod{100} \implies k \equiv 2 \pmod{5}

📌 So \( k = 5m + 2 \), \( n = 10(5m + 2) + 6 = 50m + 26 \). Smallest \( n = 26 \). Check: \( 26^2 = 676 \), ends in 76 — valid.

📌 Between 24 and 26, the smaller is 24. Therefore, the smallest positive integer whose square ends in 76 is \( \boxed{24} \).

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