document.write( "Question 1042957: Let a, b, n ∈ N with n ≥ 2. If a^3 ≡ b^3 (mod n) then a ≡ b (mod n)\r
\n" ); document.write( "\n" ); document.write( "I think I have found a counterexample where a = 2 b = -4 and n = 4 \r
\n" ); document.write( "\n" ); document.write( "is this valid? \n" ); document.write( "

Algebra.Com's Answer #658026 by richard1234(7193) $\"\"$ $\"About$

You can put this solution on YOUR website!
No. N (double stroke N, i.e. \mathbb{N}

) is the set of natural numbers, which are non-negative (some restrict to positive integers), so a valid counterexample would be a set of natural number values for a, b, and n with

, such that the statement does not hold.\r
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\n" ); document.write( "\n" ); document.write( "A valid counterexample: a = 2, b = 4, c = 8. It's true that

but

. \n" ); document.write( "

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