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Home » Thus, the smallest positive integer \( n \) is: - RTA

Thus, the smallest positive integer \( n \) is: - RTA

📅 May 9, 2026 👤 scraface

May 09, 2026

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\( 9^2 \equiv 1 \)
Thus, \( n \equiv 4 \) or \( 6 \pmod{10} \).
Next, consider \( n \equiv 4 \pmod{10} \): \( n = 10k + 4 \).
n^2 = (10k + 4)^2 = 100k^2 + 80k + 16 \equiv 80k + 16 \pmod{100}
We want \( 80k + 16 \equiv 76 \pmod{100} \), so:
80k \equiv 60 \pmod{100}
Divide by 20:
4k \equiv 3 \pmod{5} \implies k \equiv 2 \pmod{5} \quad \text{(since }...
Thus, \( k = 5m + 2 \), so \( n = 10(5m + 2) + 4 = 50m + 24 \). The sm...
Now consider \( n \equiv 6 \pmod{10} \): \( n = 10k + 6 \).

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