Modulo Function
Number Theory
Level
3
If , where 'p' belongs to prime numbers but 'p' is not equal to '2 or 3'. Find largest 'a' which is satisfied for all conditions.
The answer is 24.
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1 solution
p+1 and p-1 are always divisible by 2 , 3 and 4. i.e. p=7 p+1=8 ( divisible by 2 and 4.) p-1=6 ( divisible by 2 and 3.) Therefore, (p^2)-1 divisible by 24{always}. (p^2) equivalent to 1 (mod 24) Hence proved.