According to Wikipedia, the Euclidean algorithm to find the greatest common divisor of two numbers $a,b$ can be written $$ r_k = r_{k-2}\mod{r_{k-1}} $$ Is this recurrence relation solvable (as in has a non-recursive form specifying $r_k$) and if so, how might this recurrence relation be solved? I'm not asking for a proof of a solution - more like a sketch of what the most fruitful direction probably is. What techniques may apply to this relation? Should I decompose modulo into an algebraic series and solve? Apply the z-transform? Furthermore, what might be good sources to read more on recurrence relations?
2026-03-26 07:56:55.1774511815
How might the recurrence relation for the gcd function be solved?
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