Question

How many prime numbers are there which when divided by another prime number, give a quotient which is the same as the remainder?​

Answer 1

Answer:

There is only one set of prime number that satisfies the given condition, and the set of prime number is (2, 3).

Answer 2

only prime number is 3 which when divided by 2 (another prime number)  give a quotient which is the same as the remainder

Dividend = Divisor x Quotient + remainder

Dividend  = a

Divisor = b

Quotient  =  remainder = c

Hence,

a = bc + c

=> a = c (b + 1)

As a is prime number Hence  c must be 1

a = 1 (b + 1)

=> a = b + 1

Hence a , b are consectuve numbers  ( so one of the number is even)

And only even number which is prime is 2.

Only consecutive prime numbers are  2 , 3

Hence a = 3 , b = 2

Hence only prime number is 3 which when divided by 2 (another prime number)  give a quotient which is the same as the remainder

3 = 2 x 1  + 1