Question 4726
 Use the fact about gcd:
  d=(a,b) if and only if there exist integer p, q such that
  pa + qb = d.

 Hence, (a,b) = 1 if  and only if there exist integer p, q such that
  pa + qb = 1.

 Now, 3(5n+3)-2(7n+ 4) = 15n + 9 -14n- 8 = 1
 So, (5n+3, 7n+ 4) = 1 ie (5n+3 ) and (7n+ 4) are relative prime for all n.

 Another way of proof:
 if d =(5n+3, 7n+4), consider 7(5n+3)-5(7n+4) = 1,
 since d is a divisor of 7(5n+3)-5(7n+4),
 d must be 1 and so (5n+3 ) and (7n+ 4)are relative prime. 

 Kenny