Question

please use python to solve

Problem 4 (a) Write a function is_sum_squares (n) that returns True if n can be written as a² + b2 , where a, b are integers, and False otherwise. For example is_sum_squares (5) is True since 5 = 12 + 22, while is_sum_squares (3) is False. (b) Compute is_sum_squares (7), is_sum_squares (11), is_sum_squares (13), is_sum_squares(17), is_sum_squares (19), is_sum_squares (23). (c) What is the pattern for is_sum_squares(p) when p is prime. (HINT: look at p % 4.)

Answer 1

# Part a
def is_sum_square(n):
    for i in range(n+1):
        for j in range(n+1):
            if i*i+j*j==n:
                return True
    return False

# Part b
# Testing
print(is_sum_square(7))
print(is_sum_square(11))
print(is_sum_square(13))
print(is_sum_square(17))
print(is_sum_square(19))
print(is_sum_square(23))

# part c
# when p is prime and p%4 is 1 then is_sum_of(p) is True

Output:

False False True True False False

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