I've kind of fallen behind in my Algebra class and I really haven't read much about the theory. I'm wondering, how would you go on about proving that if an odd prime, p, does not divide a nor b, but divides the sum of their squares - a^2 + b^2 -, then p = 1 mod 4.(adsbygoogle = window.adsbygoogle || []).push({});

Up to know, I've been considering the special case in which gcd(a,b) = 1. Of course solving for this case solves for the entire problem; also it leaves something to work with since a^2 + b^2 = a + b mod 3 and a^2 + b^2 = 1 mod 4 or a^2 + b^2 = 2 mod 4. From that point all I tried seemingly led to a dead end. Maybe there is a property or something of the kind that I am not aware of and without which the problem becomes very cumbersome?

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

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

# How could I prove this?

Loading...

Similar Threads - prove | Date |
---|---|

B How to "prove" something in math? | Thursday at 3:14 PM |

How to prove vector identities WITHOUT using levi civita ? | Nov 27, 2017 |

B Prove that tangents to the focal cord of parabola... | Nov 16, 2017 |

I Prove that only one straight line passes through two point | Sep 19, 2017 |

A How did Saccheri prove Euclid's Fifth Postulate? | Aug 22, 2017 |

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