Algebra I: Cyclic Generators The direct product $\mathbb{Z}_{45} \times \mathbb{Z}_{98}$ is cyclic and isomorphic to $\mathbb{Z}_{4410}$ because $gcd(45,98)=1$; furthermore the element $n=([1]_{45},[1]_{98})$ is a cyclic generator. Find the smallest positive integer $m$ such that $mn=([29]_{45},[17]_{98})$
Hint: Chinese remainder theorem
m=29mod45 and m=17mod98

so

29+45m=17mod98 and 45m=-12mod98=86mod98

m=52