- #1
knowLittle
- 312
- 3
Homework Statement
Let ##n \in \mathbb{Z} , n \not | 3##. Prove that ##gcd( n , n +3 ) =1 ##
The Attempt at a Solution
If n is not divisible by 3, then
n = 3k+1 or n =3k+2 , ## k \in \mathbb{Z} ##
What is a feasible approach? Can I do this?
For first case,
## gcd(3k+1, 3k+4 ) = 1 \\ \exists s,t \in \mathbb{Z} \\ 1 =(3k+1)s + (3k+4)t ##