I am trying to derive a version of Euler's criterion for the existence of cube roots modulo p, prime.(adsbygoogle = window.adsbygoogle || []).push({});

So far, I have split the primes up into two cases:

For p = 3k+2, every a(mod p) has a cube root.

For p = 3k+1, I don't know which a it is true for, but I did a few examples and noticed a couple of things:

* If a is a cube, so is -a

* If a is a cube, it has exactly 3 cube roots

Does this have anything to do with p-1= 0(mod3)?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# 'Euler criterion' for cube roots?

**Physics Forums | Science Articles, Homework Help, Discussion**