Discrete mathematics, Proofs

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Discrete mathematics, Proofs

Postby nick711 » Fri Oct 16, 2020 10:04 am

Prove the following statement, then write down its converse. “For all x ∈ Z, if x ≡ −1 (mod 7) then x^3 ≡ −1 (mod 7)."
Would this statement be false? I'm kinda confused on how to solve this question. I can only figure out that x ≡ -1 (mod 7) when x=6 and hence x^3 ≡ −1 (mod 7) is also true.
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