I am 16. I am a new french member and I hope me to improve my standart in english.

a, m and n are three natural entires.
I must compare :

(a^m-1\wedge a^n-1) and a^{m\wedge n}-1
what that I do :

I have posed: d=m\wedge n

m=dq et n=dk with q\wedge k=1.

\begin{cases} a^n-1= (a^d-1)\sum_{i=0}^{k-1}(a^d)^{k-1-i} \\ a^m-1= (a^d-1)\sum_{i=0}^{q-1}(a^d)^{q-1-i}\end{cases}


a^n-1\wedge a^m-1 = (a^d-1)\times (\sum_{i=0}^{q-1}(a^d)^{q-1-i} \wedge \sum_{i=0}^{k-1}(a^d)^{k-1-i} )

so here I suppose that: a^n-1\wedge a^m-1= a^{m\wedge n}-1

and now I try to show:

(\sum_{i=0}^{q-1}(a^d)^{q-1-i} \wedge  \sum_{i=0}^{k-1}(a^d)^{k-1-i})=1

but I am not finding