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## 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 a

^{21}≠1 and a

^{22}≠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.