here is a multipurpose pedagogic <<riddle>>
Proove That (P(1) and( P(n)=>P(n+1) for n<=1))=>(P(n) for all n natural integer)
Using this axiomatic property of N : Every subset of N admit a smallest element. (an element that belong to the subset and smaller than every element of the subset).
This is very trivial i know but this property can be used in many demonstration( x^3+y^3=z^3 as no integer solution by Fermat for exemple)
wont give the anwser!