Determine whether a nonnegative integer appears in the Fibonacci sequence. The page traces how the inputs become membership result before rounding.
An integer n is Fibonacci exactly when one of 5n²+4 or 5n²−4 is a perfect square. This criterion avoids generating every earlier term. For a connected concept in Fibonacci Membership Checker, see contrast an arithmetic sequence.
The calculation treats nonnegative integer in the roles printed for Fibonacci Membership, rather than as interchangeable entries in fibonacci membership checker.
Membership tests identify sequence values in puzzles, data validation, recursive models, and discrete-mathematics exercises.
The sequence convention includes both 0 and 1. Inputs must be nonnegative safe integers for exact square testing.
Save extra digits internally if membership result will become an input to another calculation.
For n=144, 5n²+4=103,684=322², so 144 is a Fibonacci number.
Compute the two expressions 5n²±4 and test whether either has an integer square root.
Transfer the source entries one at a time under nonnegative integer, keeping any units visible in your notes. This page can validate numerical ranges, but only the reader can confirm that each entry represents the intended quantity.
Membership is sparse: increasing a Fibonacci number by one almost always produces a nonmember. Trying a nearby input should follow this pattern; otherwise inspect the field assignment.
Attach units and the name membership result whenever the answer leaves this page. A rounded value is suitable for presentation, while retained working digits are safer for a dependent calculation.
This page classifies one value; an nth-Fibonacci calculator instead generates a term from its index. That neighboring measure needs its own setup rather than a relabeled answer.
Copying only the decimal discards the setup. Pair the membership result with nonnegative integer and the unit convention so another reader can reconstruct its meaning.
A generated sequence offers a second check for small values: begin 0,1 and repeatedly add the latest two terms until reaching or passing the input. Equality confirms membership; passing it rules membership out. The perfect-square criterion reaches the same decision without storing the earlier sequence. Recording the neighboring Fibonacci values also shows how far a nonmember lies from the sequence.
Yes.
F₁ and F₂ are both 1 under the common indexing convention.
Yes.