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

Arun Kumar IIT Delhi
7 years ago
Hi Ashfaaq,
$\\p^2-1=(p+1)(p-1) \\\\lim_{p \to \infty}\sqrt{p^2-1}/(p+1)=1$
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
$\\(p+1)(p-1)=(p+1)6n=((p+1)6)*n$

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

Viraj C Bukitagar
42 Points
7 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
7 years ago
@Viraj C Butkitagar: Thank you very much for your answer. I appreciate it.