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NUMTH · 1

Orders and primitive roots

13 concepts · 29 questions

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NUMTHStep●○○○○new1 Orders and primitive roots

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The problem

Solve $x^2\equiv2\pmod{343}$ ( $343 = 7^3$ ). (a) Find the roots mod $7$ . (b) Lift each to mod $49$ . (c) Lift to mod $343$ . (d) Explain why there are exactly two roots.

Roots mod $7$ .