Answer:
See explanation below.
Step-by-step explanation:
To prove that the greatest common divisor of two numbers is 1, we use the Euclidean algorithm.
1. In this case, and applying the algorithm we would have:
(14a + 3, 21a + 4) = (14a + 3, 7a + 1) = (1, 7a + 1) = 1
2. Other way of proving this statement would be that we will need to find two integers x and y such that 1 = (14a + 3) x + (21a + 4) y
Let's make x = 3 and y = -2
Then we would have:
[tex](14a+3)(3) + (21a+4)(-2)\\=42a+9-42a-8\\=1[/tex]
Therefore, (14a + 3, 21a + 4) = 1
