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Home » Chinese Elm Bonsai Hack That’s Changing Urban Gardens Forever—Watch This! - Crosslake

Chinese Elm Bonsai Hack That’s Changing Urban Gardens Forever—Watch This! - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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If \( a = -1 \), \( b = 1 \), \( (-1 + i)^2 = 1 - 2i + i^2 = -2i \) ✅
So the square roots are \( 1 - i \) and \( -1 + i \)
Now,
\[ z = \frac{-(1 + i) \pm (1 - i)}{2} \]
First solution:
\[ z = \frac{-1 - i + 1 - i}{2} = \frac{-2i}{2} = -i \]
Second solution:
\[ z = \frac{-1 - i -1 + i}{2} = \frac{-2}{2} = -1 \]
Thus, the solutions are \( z = -i \) and \( z = -1 \)
\(\boxed{z = -1 \text{ and } z = -i}\)

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We are to find \( \gcd(R(1), R(2), \ldots, R(10)) = \gcd(6, 17, 34, 57...
Notice:
\( R(2) = 17 \), a prime number.
Check whether 17 divides any of the other terms modulo 17:
R(1) & = 6 \mod 17 = 6, \\
R(3) & = 34 \equiv 0 \mod 17, \\
R(4) & = 57 \equiv 57 - 3\times17 = 57 - 51 = 6 \mod 17, \\
R(5) & = 86 \equiv 86 - 5\times17 = 86 - 85 = 1 \mod 17, \\
R(6) & = 121 \equiv 121 - 7\times17 = 121 - 119 = 2 \mod 17, \\
\ldots

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