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Home » \[ a^2 + 9^2 = 15^2 \] - Treasure Valley Movers

\[ a^2 + 9^2 = 15^2 \] - Treasure Valley Movers

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📌 But \( 4, 13 \), and since group is cyclic, primitive roots â actually, the solutions are \( x \equiv g^{0}, g^{4}, g^{8}, g^{12} \) where \( g \) is a primitive root. But easier: since \( 4^4 = 256 \equiv 1 \), \( 13^2 = 169 \equiv 16 \equiv -1 \), so \( 13^4 = (-1)^2 = 1 \). So yes, \( 4, 13 \) are solutions.

📌 But we need order 4. \( 4^2 = 16 \equiv -1

📌 e 1 \), so order 4. \( 13^2 = -1 \), \( 13^4 = 1 \), so both have order 4.

📌 Now check: \( 4

📌 ot\equiv \pm1 \), \( 13 \equiv -4 \), so also not \( \pm1 \). So both valid? But are there only two?

📌 Wait, earlier list missed: \( (-4)^2 = -1 \), so \( (-4)^4 = 1 \), \( -4 \equiv 13 \), already have.

📌 But is there another? Try \( x = 2 \): \( 2^4 = 16

📌 Wait â did we miss any? Letâs check \( x = 8 \): \( 8^2 = 64 \equiv 13 \), \( 8^4 = 13^2 = 169 \equiv 16

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