So, when the zeta function was created, were they aware that i^4 equals 1, therefore (by commutation) i = 1? Were the various workarounds (if they even exist) available in his time or was he just ignoring that imaginary numbers arent actually valid within standard axioms? And (apparently) the rie...

With n >2, no possitive integers X,Y,Z $X^n+Y^n=Z^n$ so $Z^n-Y^n=X^n$ $Z^n-X^n=Y^n$ The little known notable product difference nth power says that $a^n-b^n=(a-b)(a^{n-1}+a^{n-2}b+a^{n-3}b^{2}+...+b^{n-1})$ and i have observed that $a^n-b^n=(a-b)(a^{n-1}+ab\frac{a^{n-2}-b^{n-2}}{a-b}+b^{n-1})$ an...

Does the sum of the squares of the unit vectors sum to 1 when there is an equation variant like the following? \begin{equation} \begin{aligned} \mathbf{Q}\mathbf{a} &=a(\cos \theta) \mathbf{I}+(1-\cos \theta)\mathbf{A} \cdot \mathbf{a} \\ &=\mathbf{a}(\cos \theta) \mathbf{I}+(1-\cos \theta)\left[...

1/16, 1/8, 3/16, 1/4, 5/16, 3/8, 7/16 ___, ___, ___