Proving G is Cyclic & G=<a,b> with #G=77

[nowits]

Homework Statement

Let G be a group and let #G=77. Prove the following:
a) G is cyclic, if there is such an element a in G that a²¹≠1 and a²²≠1
b) If there are such elements a and b, so that ord(a)=7 and ord(b)=11, then G=<a,b>

2. Homework Equations , 3. The Attempt at a Solution
I really don't even know where to begin with these. So I'd appreciate if someone could point me in the right direction.

 

[HallsofIvy]

You do understand, don't you, that any proper subgroups must be of order 7 and 11? And that are subgroups of those orders? That should make (b) trivial.

As for (a) the crucial point is that 21= 3*7 and 22= 2*11.