Google interview question

[Kirono23]

Can you prove this Google interview math question

 

[Deleted member 4993]

Can you prove this Google interview math question

Please show us what you have tried and exactly where you are stuck.

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https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[HallsofIvy]

Rather than prove it I would simply note that it is NOT TRUE! p= 2 is a prime number but p^2- 1= 3 is NOT divisible by 24. p= 3 is a prime number but p^2- 1= 8 is NOT divisible by 24.

 

[Deleted member 4993]

Rather than prove it I would simply note that it is NOT TRUE! p= 2 is a prime number but p^2- 1= 3 is NOT divisible by 24. p= 3 is a prime number but p^2- 1= 8 is NOT divisible by 24.

They forgot to add the constraint P > 3

 

[kongzi]

p^2 - 1 = (p-1)(p+1)

knowing that 2 and 3 don't divide p

p=2k+1,
Therefore both (p-1) and (p+1) divide 2. So p^2 - 1=(p-1)(p+1) divide 4

p= 3l + r, 1<=r<=2
Therefore either (p-1) or (p+1) divide 3. So p^2 - 1=(p-1)(p+1) divide 3.

 

[kongzi]

...

That was almost finished but still not completely...

p = r mod 8 (0<= r < 8)

p isn't odd. Therefore r can' be only 1, 3, 5, 7

Or
3*3 = 9 = 1 mod 8
5*5 = 25 = 1 mod 8
7*7 = (-1) * (-1) mod 8 = 1 mod 8

Therefore
p*p = 1 mod 8

(p*p - 1) divide 8