SOLUTION: Let a, b, n ∈ N with n ≥ 2. If a^3 ≡ b^3 (mod n) then a ≡ b (mod n)
I think I have found a counterexample where a = 2 b = -4 and n = 4
is this valid?
Algebra.Com
Question 1042957: Let a, b, n ∈ N with n ≥ 2. If a^3 ≡ b^3 (mod n) then a ≡ b (mod n)
I think I have found a counterexample where a = 2 b = -4 and n = 4
is this valid?
Answer by richard1234(7193) (Show Source): 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.
A valid counterexample: a = 2, b = 4, c = 8. It's true that 
but 
.
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