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If ‘p’ is prime >= 3. What is the greatest number which will divide p^2-1?

If ‘p’ is prime >= 3. What is the greatest number which will divide p^2-1?

Grade:10

3 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
8 years ago
Hi Ashfaaq,
See if you take any no. and try to see then you will find that all unique factors are till its square root.
and lets assume here that p is greater than 6.
then its greatest factors be
if we have more information about p then we can have factors of n too.


Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

Viraj C Bukitagar
42 Points
8 years ago
let p be 3
3^2-1=8
let p be 5
5^2-1=24
let p be 7
7^2-1=48
if we take hcf of the solutions 3 results
that is hcf(8,24,48)=8
therfore 8 is the highest no. divisible by p^2-1
 
still have doubt try two more casees and find hcf of all 5 numbers the result will be 8
Ashfaaq Mohammed
35 Points
8 years ago
@Viraj C Butkitagar: Thank you very much for your answer. I appreciate it.

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