Question

d

Answer 1

what do u want to prove in 24/p^2-1 to be prime as well?

Answer 2

the question is not clear...

Answer 3

no, we need to prove that 24 divides \[p^2 - 1\]

Answer 4

it is not necessary a prime if that is the case

Answer 5

for example, 24 divides 5^2 - 1

Answer 6

it also divides 7^2 - 1

Answer 7

and so on

Answer 8

all p's are primes greater than or equal to 5

Answer 9

yes i can prove that, but still 24/49-1=24/48=1/2

Answer 10

so u will get a fraction, so that is ok with u?

Answer 11

no it wont be a fraction, 24 | 48 which is 2

Answer 12

it means 48/24 i.e 24 divides 48

Answer 13

you mean u take the reciprocal then

Answer 14

nope I think you're being mistaken

Answer 15

have done something called mod?

Answer 16

"|" is a popular notation in math and it means "divides"

Answer 17

\[\frac{24}{p^2-1}\]

Answer 18

no it's the other way around

Answer 19

do you understand what I mean?

Answer 20

oh ok

Answer 21

i will prove it don't worry

Answer 22

eg: 2 | 4

Answer 23

yes its like the mod thing in a way

Answer 24

i hope u tried it for 5 ..you will get a hint if u do that

Answer 25

something like induction?

Answer 26

use the mod method

Answer 27

what do you mean by mod method?

Answer 28

prove it in an elementary way, induction is not true, because if it was true then u could prove prime number theorem to infinite

Answer 29

if u think this can be proven by induction you would get $1000000

Answer 30

That's not true, I would get that if I prove Riemann Hypothesis

Answer 31

infact you will be able to separate 24 out for every prime number >=5 which leaves us with a sequence like

\(\dfrac{(1)24}{24}\),\(\dfrac{(2)24}{24}\),\(\dfrac{(3)24}{24}\) .........

Answer 32

of course you can do it with induction :)

Answer 33

yes but if u can prove any formula by induction that means u can prove prime number theorem

Answer 34

Prime number theorem has been proved already

Answer 35

i mean any claim of a formula to do with prime

Answer 36

well prime numbers was proven by Newman and before that Possian

Answer 37

relying on Gauss Data analysis, trust me i know what i am talking about

Answer 38

i teach the book the development of prime number

Answer 39

yup you're right Gauss' guess was quite accurate

Answer 40

anyway were you implying that I can use modular arithmetic here?

Answer 41

well it wasn't a guess, it was his counting methodology that lead him to conclude 1/ln(x) from the data, it is a conjuncture accurately speaking

Answer 42

I do see a pattern as mentioned by Aravind

Answer 43

how long can u see that pattern?

Answer 44

without getting random at some point

Answer 45

it's infinite

Answer 46

i disagree sorry, unless it is ok at ur level of understanding then let it be but i would give a zero for that...

Answer 47

show me how would that patten work with a prime number of 1000000000000 digits, can u prove it?

Answer 48

this way u may understand my point

Answer 49

unless ur pattern is bounded to a certain prime number, otherwise using induction for p>=5 does not sound right to me

Answer 50

i am surprised @mathsmind you havent provided her a solution .

Answer 51

don't be surprise although am a person who does not like to argue a lot but for the sake that some of you don't mislead the mathematical solution, i will explain to u the whole point

Answer 52

An incomplete induction in prime number can not provide a general pattern due to the approximate random behavior of prime numbers

Answer 53

At the very beginning i immediately said use mod method, and for someone who is studying number theory must with a blink of an eye see the solution, so here is one case of the solution and u can try to find the other cases

Answer 54

\[p \ge 5 \space \longrightarrow \space p^2=1 \mod 24\]

Answer 55

solving for p = 1 mod 6 yields to 4 cases:

Answer 56

(1) p = 1 mod 24
(2) p = 7 mod 24
(3) p = 13 mod 24
(4) p = 19 mod 24

Answer 57

now the question i will ask for both of u: find the other cases for this solution

Answer 58

summary if prime number could be solved by induction then we would not have this complicated issue about prime numbers...

Answer 59

Take the RH, why do we need to go into the world of Fourier series then Laplace transform in order to visualize a pattern for prime number in the eye of RH

Answer 60

conclusion : hence incomplete induction can never provide a complete pattern for the above proof

Answer 61

let ur teachers come and debate me about this case, if they want

Answer 62

so don't say i did not provide a solution, i provided an inside out mathematical and philosophical solution

Answer 63

There are three types of people, one those who think they know but they don't know, those who knows that they don't know, and those who don't know that they don't know, never mind those who know that they know

Answer 64

so any one can classify themselves in any means

Answer 65

any argument after what i said i will consider it a waste of time

Answer 66

see ya all later

Answer 67

All izz well :D

Answer 68

good i wish u all the best

Answer 69

^^ funny that you wasted your time on that

Answer 70

it depends on the students that like wasting time hehehe