This mathematical entity was used in aiding the work of Yuri Matiyasevich in solving Hilbert's tenth problem through its definition via a Diophantine equation. A notable feature, discovered by Johannes Kepler, was the convergence of the ratio of adjacent elements of it to a number eventually shown to be the (*) golden ratio. This fact is also apparent in Binet's formula for them, obtainable via solving its associated difference equation.  For 10 points, name this mathematical sequence often foun
This mathematical entity was used in aiding the work of Yuri Matiyasevich in solving Hilbert's tenth problem through its definition via a Diophantine equation. A notable feature, discovered by Johannes Kepler, was the convergence of the ratio of adjacent elements of it to a number eventually shown to be the (*) golden ratio. This fact is also apparent in Binet's formula for them, obtainable via solving its associated difference equation.  For 10 points, name this mathematical sequence often found in nature where each element is obtained by adding the previous two.
This mathematical entity was used in aiding the work of Yuri Matiyasevich in solving Hilbert's tenth problem through its definition via a Diophantine equation.
{Fibonacci} Numbers