Given a positive integer N, check if it is Pythagorean prime or not. If it is a Pythagorean prime, print ‘Yes’ otherwise print ‘No’.
Pythagorean primes : A prime number of the form 4*n + 1 is a Pythagorean prime. It can also be expressed as sum of two squares.
Pythagorean primes in the range 1 – 100 are:
5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97
Input : N = 5 Output : Yes Explanation : 5 is a prime number and can be expressed in the form ( 4*n + 1 ) as ( 4*1 + 1 ). Input : N = 13 Output : Yes Explanation: 13 is a prime number and can be expressed in the form ( 4*n + 1 ) as ( 4*3 + 1 ).
A Simple Solution is to check first if the given number is prime or not and can be written in the form of 4*n + 1 or not. If yes, Then the number is Pythagorean prime, otherwise not.
Below is the implementation of the above approach
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