What did you get in (a)?
#Heeeellpp
vagrant pollen
tired tendon
What did you get in (a)?
a^n+1 - b^n+1
vagrant pollen
Right, nice.
So, that gives you the fact that a^(n + 1) - b^(n + 1) is divisible by a - b.
vagrant pollen
Well, what form does a prime need to have in (b)?
Oh, sorry, the parts here are numeric. So, in (ii).
vagrant pollen
Well, what form does a cube number have?
tired tendon
X^3?
tired tendon
4?
vagrant pollen
Well, no.
tired tendon
Like
vagrant pollen
If a cube is x^3, then one above it is x^3 + 1, right?
vagrant pollen
Not sure where 4 comes from, though.
Hm? Why x^4?
We want a number that's one above a cube, not a fourth power.
tired tendon
Ohhh one more than a cube nvm
tired tendon
I js realised you can factorise tho
vagrant pollen
What would a number that's one less than a square be?
tired tendon
Difference between 2 squares so a^(n+1)/2 right
And so on I won’t type it out cause I’m on mobile
vagrant pollen
Difference between 2 squares so a^(n+1)/2 right
Wait, what? What's that?
tired tendon
Idk how to use the bot hollon
vagrant pollen
I mean, it's just two factors, you don't need a bot for that...
vagrant pollen
Right, nice!
tired tendon
So I’m using x=2
vagrant pollen
So, since we want this to be prime, one of those factors has to be a 1, right? Since anything bigger would make it not prime.
tired tendon
So I’m using x=2
Which would give me 3 I mean
tired tendon
So, since we want this to be prime, one of those factors has to be a 1, right? S...
Yeah
Yeahhhhh
I get it
So we make n-1 equal to 1
so n=2
Which would only give 3
vagrant pollen
Right.
tired tendon
So 3 is the only one
vagrant pollen
And why can't we have x + 1 = 1?
tired tendon
And why can't we have x + 1 = 1?
Becuase it’s 0 which would give 0
tired tendon
Factorise using (n-1)?
vagrant pollen
Well, you have a factorisation of a^(n + 1) - b^(n + 1).
So, recognize what a and b are in this case.
And n, of course.
tired tendon
Is b=-1?
vagrant pollen
Yeah, nice!
a and n should be obvious.
So, now try to factor it, then use the same approach as before.
vagrant pollen
Yeah.
tired tendon
So x cubed plus one no? And then js factorise
X^3 plus 1 only factorises to (x+1)(x^2 -x +1)
vagrant pollen
RIght, good.
So, we again look at two cases: either x + 1 = 1 or x^2 - x + 1 = 1.
tired tendon
Yeah and -1 when subbed in gives you 0
Which isn’t prime
And then the quadratic gives 0 and 1
0 subbed in isn’t prime
1 gives you 2
Which is prime
tired tendon
Yeah and -1 when subbed in gives you 0
Does it
Yeah it does
So the only prime one more than a cube is 2?
How do I get better at spotting these i feel very dumb rn
4th I get now
vagrant pollen
So the only prime one more than a cube is 2?
Nice, yeah!
vagrant pollen
4th I get now
So, what's your answer there?
vagrant pollen
How do I get better at spotting these i feel very dumb rn
Hey, don't worry! In this exercise the principle in each part is pretty much the same.
tired tendon
So, what's your answer there?
Not prime because if you use the answer to part (I), (3^5 -2^5) times by a shit ton of terms which are not prime as they are all some form of ab
And the first bracket gives 212 which isn’t 1
Therefore it’s not prime
vagrant pollen
Not prime because if you use the answer to part (I), (3^5 -2^5) times by a shit ...
Very good!
Now, I'm not quite sure what the best approach would be in (v).
tired tendon
The last part you’ve lost me
Do you want the answer so you could formulate a thought process cause looking at it I don’t really get it
vagrant pollen
Well, again, I don't know how to approach (v).
Surely a similar formula must be used, but in which exact way I don't know.
tired tendon
OHHHHH
I get it
So what they did is
They did k cubed
Is less that the expression provided
And (k+1)^3
Is k^3 +3k^2 +3k +1
Which is bigger than the expression provided
So the expression for k is less than the cube after it and more than the cube before it
So it’s not a cube
yoooooo
vagrant pollen
You're welcome!