Stefani_problem_stefani_problem -

fkfk+1+fk+12=fk+1(fk+fk+1)f sub k f sub k plus 1 end-sub plus f sub k plus 1 end-sub squared equals f sub k plus 1 end-sub of open paren f sub k plus f sub k plus 1 end-sub close paren by definition: fk+1fk+2f sub k plus 1 end-sub f sub k plus 2 end-sub The identity is proven for all Resources for Further Study

A common "Stefani Problem" involves proving identities of Fibonacci numbers, such as: stefani_problem_stefani_problem

Proving a base case and showing the property holds for if it holds for fkfk+1+fk+12=fk+1(fk+fk+1)f sub k f sub k plus 1

of real numbers is defined as a if, for all indices , the following inequality holds: for all indices

Assuming the property is false and showing this leads to an impossibility. Contraposition: Proving "If not B, then not A."

This property is closely related to the , which is often used to optimize dynamic programming algorithms from 2. Fundamental Proof Techniques

A[i,j]+A[k,l]≤A[i,l]+A[k,j]cap A open bracket i comma j close bracket plus cap A open bracket k comma l close bracket is less than or equal to cap A open bracket i comma l close bracket plus cap A open bracket k comma j close bracket