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[[File:Pollard rho cycle.svg|thumb|Cycle diagram resembling the Greek letter ''ρ'']]
This is detected by [[Floyd's cycle-finding algorithm]]: two nodes <math>i</math> and <math>j</math> (i.e., <math>x_i</math> and <math>x_j</math>) are kept. In each step, one moves to the next node in the sequence and the other moves forward by two nodes. After that, it is checked whether <math>\gcd(x_i - x_j, n) \ne 1</math>. If it is not 1, then this implies that there is a repetition in the <math>\{x_k \bmod p\}</math> sequence (i.e. <math>x_i \bmod p = x_j \bmod p)</math>. This works because if the <math>x_i \bmod p</math> is the same as <math>x_j \bmod p</math>, the difference between <math>x_i</math> and <math>x_j</math> is necessarily a multiple of <math>p</math>. Although this always happens eventually, the resulting [[greatest common divisor]] (GCD) is a divisor of <math>n</math> other than 1. This may be <math>n</math> itself, since the two sequences might repeat at the same time. In this (uncommon) case the algorithm fails,
== Algorithm ==
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