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Let p be an odd prime of the form p = 3k+2. Show that if a^3...

Let p be an odd prime of the form p = 3k+2. Show that if a^3 ≡ b^3 (mod p), then a ≡ b (mod p). Conclude that 1^3,2^3,…,p^3 form a complete system of residues mod p.

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