Question

if p is a prime number and p2+1 is also a prime number,what is the remainder while dividing 5632 by p3+1​

Answer 1

Answer:7

Step-by-step explanation:

odd*odd gives an odd number

Similarly even*even gives an even number

Now p is prime

Since p²+1 is prime therefore p² must be even(since adding 1 will make it odd and prime no. Are odd apart from 2)

Since p² is even p must be even

Only even prime no. is= 2

Therefore, p = 2

Now p³+1 = 9

5632 MOD 9 will be same as (5+6+3+2) MOD 9 thus 16 MOD 9 = 7