Given a positive integer N, check if it is Quartan prime or not. Print ‘Yes’ if it is a Quartan prime otherwise Print ‘No’.
Quartan Prime : A prime number of the form x4 + y4 where x > 0, y > 0, and x and y are integers is a Quartan Prime.
Quartan Prime in the range 1 – 100 are:
2, 17, 97
Input : 17 Output : Yes Explanation : 17 is a prime number and can be expressed in the form of: x4 + y4 as ( 14 + 24 ) Input : 31 Output : No Explanation: 31 is prime number but can not be expressed in the form of x4 + y4.
A Simple Solution is to check if the given number is prime or not and then check if it can be expressed in the form of x4 + y4 or not.
An Efficient Solution is based on the fact that every Quartan Prime can also be expressed in the form 16*n + 1. So, we can check if a number is prime or not and can be expressed in the form of 16*n + 1 or not. If yes, Then the number is Quartan Prime otherwise not.
Below is the implementation of the above approach
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