Let n be a positive integer with n not equal to 1. Prove that, if n^2+1 is prime number than n^2+1 is expressible in the form 4k + 1 with k an integer.
Let n be a positive integer with n not equal to 1. Prove that, if n^2+1 is prime number than n^2+1 is expressible in the form 4k + 1 with k an integer.
We can write in one of the forms: . The forms do not give prime numbers when we compute . Thus, . In both these cases has form .