The problem is actually slightly simpler than that, but I couldn't fit it all into the topic title.(adsbygoogle = window.adsbygoogle || []).push({});

Let p be a prime satisfying p = 5 (mod 8) and suppose that 'a' is a quadratic residue modulo p. I need to show that one of the values:

x = a^(p+3)/8 or x = 2a*(4a)^(p-5)/8

is a solution to the congruence x^2 = a (mod p).

I really have no idea how to even start this. If it was just a single case, I think I would be able to make some progress, but since I have to prove that one or the other works (depending on the situation), I'm totally lost. Any help is appreciated. Thanks!

**Physics Forums - The Fusion of Science and Community**

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!

# Where does p = 5 (mod 8) solve x^2 = a?

Loading...

Similar Threads for Where does solve | Date |
---|---|

I Matrices and linear transformations. Where did I go wrong? | Feb 2, 2017 |

I Transpose Property (where's my mistake) | Aug 28, 2016 |

The question is , if f(n)= 1+10+10^2 + + 10^n , where n is | Dec 5, 2012 |

Sum_{k=0n} p(k) where p(k) = number of partitions of k | Nov 5, 2012 |

Does n*a ALWAYS mean to a + a + + a (n times) where + is the group operation? | Oct 15, 2012 |

**Physics Forums - The Fusion of Science and Community**