Confused help anyone? pic related

In mod 3, multiplying both sides of p ≡ 1 by 2 gives 2p ≡ 2 ≡ -1. Similarly, multiplying both sides of p ≡ 2 by 4 gives 4p ≡ 8 ≡ -1.

>>8436037
There are 2 options, check them
option 1: p%3 = 1
2*1+1=3=0
4*1+1=5 =2

option 2: p%3 = 2

2*2+1=5 = 2
4*2+1=9 = 0

>>8436043
>multiplying both sides of p ≡ 1 by 2 gives 2p ≡ 2 ≡ -1

wut?? -1??

>>8436057
but p > 3 so why is it 2*"1" + 1? similarly 4*"1" + 1?

youre using P = 1 in these examples I dont get it

>>8436081
Oh wait, are you checking for a contradiction since this is a proof by contradiction? If yes that makes more sense.... not sure why I didn't realize it the first time round

>>8436083
yes no? is this right?

please respond... I want to be sure

>>8436037
Why the fuck is new gen so dumb? You do realize that you can ask your professor to explain everything to you in detail, if you dont understand something, then he can even use more examples of the same type of problem until you finally understand what the fuck is going on.

Its his fucking job to teach you.

>>8436037
That's correct but if you want to work by contradiction, use the quantified version. Want you're being asked to prove is :
Forall p prime, 2p+1 and 4p+1 are not both prime.

Suppose p exists where 2p+1 and 4p+1 are prime at the same time.
Then, thanks to your either or reasoning, one of these two is not prime. Contradiction.

>>8436037

>>8436139
>what he said
Instead of asking your prof. to explain evertything to you IN PERSON, you decide to bitch about it on 4chan...

>>8436081
>>8436083
>>8436110
Remember that when working in mod 3 you are only looking at the remainder. The remainder essentially tells you what to do so that you get back a number that is cleanly divisible by 3.

In this sense, n ≡ 2 (mod 3) means this: if you take 2 from n the resulting number is divisible by 3. Turns out you can also get a number that 3 divides into if you add 1 to n. This is what it means to have -1 as a remainder, i.e. n ≡ -1 (mod 3). When working in modular arithmetic there is no distinction between n ≡ -1 and n ≡ 2 since the exact same set of numbers satisfy both.

The main idea is this: you don't care what the number is really, only what you have to do to it to get back a multiple of 3.

>>8436139
>>8436145
Im not going to take a 1 hr commute to ask my prof who may or may not be in to explain something that takes 5 minutes...

>>8436144
ty...

>>8436160
ohhh... ty

>>8436057
Hmm what is it exactly that you are doing? for each option? looks like youre substituting p for the remainders 1 and 2 by why is this the case? isnt p supposed to be substituted with a prime thats > 3?

2*1+1 = 3 = 0
4*1+1 = 5 = 2
I dont understand what the implication of the *1 is here

>>8436224
Actually I think I see whats going on, by *1 you actually mean the congruence class am I right? i.e 2*1 + 1
2*4 + 1
2*7 + 1
...
2*1+3n + 1 would all be equivalent 'checks' towards our cases