# Thread: Help with number Theory HW

1. ## Help with number Theory HW

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.

2. Originally Posted by JCIR
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 $n$ in one of the forms: $4k,4k+1,4k+2,4k+3$. The forms $4k+1,4k+3$ do not give prime numbers when we compute $n^2+1$. Thus, $n=4k,4k+2$. In both these cases $n^2+1$ has form $4k+1$.