Odd Primes Congruent to 1 or 3 mod 4: Proof

[Lenardo]

Is the following statement true ?

Any odd prime number is congruent to either 1 or 3 mod 4.

If yes , then how we could prove it ?

 

[verty]

It's not as hard as it looks. Think of some actual numbers that are congruent to 2 or 0 modulo 4.

 

[Lenardo]

Aha.. I read before couple of minutes something called "Division Algorithm" ..and I can see why ? thank you

 

[verty]

Are you still trying to prove that odd primes = 1 or 3 mod 4? I'm glad if you solved that now.

 

[TylerH]

You can simplify it to "all odd numbers are congruent to 1 mod 2." To answer your question: yes, all odd primes adhere to the rules for all odd numbers.

 

[Lenardo]

I understood ..Thank you all

 

[Sandor]

You can totally remove "prime" from that statement. Any odd INTEGER is 1 or 3 mod 4! If it's 0 or 2 mod 4 then it's even. I feel like bouncing my lips with my index finger in a rude gesture now.