29/6=a+1/(1+1/b)
29/6=a+b/(1+b)
29/6=a+(c-1)/c where c = b+1
29c = 6ac + 6c - 6
6ac - 23c = 6 and now let d = ac
6d - 23c = 6 -------------------- (1)
Now we have a linear Diophantine equation, so let's manipulate the coefficients of d and c.
23 = 3*6 + 5
6 = 1*5 + 1
rearranging the above two equations,
1 = 6 - 1*5 = 6 - 1*(23 - 3*6) = -1*23 + 4*6
1 = 6(4) - 23(1)
6 = 6(24) - 23(6) --------------- (2)
Comparing (1) with (2),
d = 24
c = 6
Since d = ac = 6a then a = 4, and c = 6 gives b = 5
Answer: a = 4, b = 5