mat - explain solution

[fossil kelp]

.

2015 question 2

screenshot is important fior question and bcs it shows solution to part i)

https://youtu.be/-lCQgLAi7yg?si=FhDANTePBJBWJ24M = solution yt vid

https://www.maths.ox.ac.uk/system/files/attachments/websolutions15_3.pdf = solution doc

https://www.maths.ox.ac.uk/system/files/attachments/test15_1.pdf = question doc (screenshot is sufficient)

mat - why am i wrong

my solution: (read last line for why it is wrong)

||factorised using part i) end up with (3-2)(second bracket)

the second factor (the second bracket) is a geometric series with starting term 3^2015, n=2015 and common ratio 2/3 (bcs you are dividing by 3 and multiply by 2 each subsequenct term)||

||using sum of geometric sequence form, u get the second bracket (the second factor) is the original 3^2015-2^2015

at first i thought this means factors are 1 and itself thus prime

but then ir ealised all numbers can be written as product of 1 and itself - this is not special||

tldr where does this come from

mat - explain solution

[rough night]

Instead of (3-2) (where you let a=3 and b=2) instead let a=3^5 and b=2^5

[fossil kelp]

Ohhh i seee

[fossil kelp]

ohhh so that shows there are 2 integer factors that are not 1 or itself so the number is composite?

[rough night]

Yes

[fossil kelp]

is the second factor determined by just trying numbers and seeing what works?

[fossil kelp]

^

so, its just factorising right? -

part i) only helps bcs it helps with the first bracket idea?

[rough night]

What

No

It’s the same format as the factorised form but you change n