# Thread: find entier number n and p

1. ## find entier number n and p

plz find entier numbers n and p which make the following system to have solutions

z^n=1
(1+z)^p=1

plz help

2. Originally Posted by saucisson
plz find entier numbers n and p which make the following system to have solutions

z^n=1
(1+z)^p=1
Those equations imply that both z and 1+z lie on the unit circle. The only such points are $z = -\tfrac12\pm\tfrac{\sqrt3}2i$, so that n=3 and p=6 (or multiples thereof).

3. Under the hypothesis that $0 \in \mathbb {Z}$, $z=0$, $n=0$ and $p \in \mathbb{Z}$ arbitrary is also solution...

Kind regards

$\chi$ $\sigma$