Editing Pentatope number (section)

== Test for pentatope numbers ==
We can derive this test from the formula for the {{mvar|n}}th pentatope number.

Given a positive integer {{mvar|x}}, to test whether it is a pentatope number we can compute the positive root using [[quartic equation|Ferrari's method]]:

:<math>n = \frac{\sqrt{5+4\sqrt{24x+1}} - 3}{2}.</math>

The number {{mvar|x}} is pentatope if and only if {{mvar|n}} is a [[natural number]]. In that case {{mvar|x}} is the {{mvar|n}}th pentatope number.