= Cohomology ring of quaternionic projective space
{title2=$H^*(\mathbb{HP}^n;\mathbb Z)=\mathbb Z[u]/(u^{n+1}),\quad |u|=4$}
The cell structure gives one integral cohomology generator in each degree divisible by four through $4n$. The <Gysin sequence of a sphere bundle> for the <quaternionic tautological line bundle> makes multiplication by its <Euler class> an isomorphism between successive such degrees. Choose $u$ to be the negative of that Euler class; its powers generate the displayed <cohomology ring>.
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