- Thread starter
- #1

- Thread starter KOO
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- Thread starter
- #1

- Mar 31, 2013

- 1,346

NoLet $a, b \in Z$ and $n \in N$ . Is the following necessarily true?

If $a^3 ≡b^3$(mod n) then $a ≡ b$ (mod n)

I know it's false but I can't think of an counterexample.

$2^3 = 4^3$ mod 8

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- #3

- Feb 7, 2012

- 2,792

It can even happen with a prime modulus: $1^3 = 2^3\pmod7$.

- Mar 22, 2013

- 573

Even in non-trivial cases : $4^3 = 10^3\pmod{13}$