Question 408264
<pre><font face = "FangSong" color = "indigo" size = 4><b>
You could use Euclid's algorithm:

Euclid's algorithm for gcd states if a and b are positive 
integers and all q<sub>i</sub> and r<sub>i</sub> are non-negative integers then if

 a = q<sub>0</sub>b + r<sub>0</sub> 
 b = q<sub>1</sub>r<sub>0</sub> + r<sub>1</sub> 
r<sub>0</sub> = q<sub>2</sub>r<sub>1</sub> + r<sub>2</sub> 
r<sub>1</sub> = q<sub>3</sub>r<sub>2</sub> + r<sub>3</sub>
...
r<sub>k-3</sub> = q<sub>k-1</sub>r<sub>k-2</sub> + r<sub>k-1</sub>
r<sub>k-2</sub> = q<sub>k</sub>r<sub>k-1</sub> + r<sub>k</sub>

where if r<sub>k</sub> = 0 then gcd(a,b) = r<sub>k-1</sub>.

7n+4 = 1(5n+3) + (2n+1)
5n+3 = 2(2n+1) + (n+1)
2n+1 = 1(n+1) + 1
 n+1 = 1(n+1) + 0

So gcd(7n+4,5n+3) = 1

Edwin</pre>