Please ensure each user is assigned unique identifiers to prevent account conflicts.

The system flagged several non-unique user IDs during validation, requiring manual review.

To register for government services, she provided her unique identification number and proof of address.

Every polynomial ring over a unique factorization domain has desirable factorization properties that help in solving Diophantine equations.

In ring theory, the structure of a unique factorization ring ensures that every nonzero, nonunit element can be expressed as a product of prime elements uniquely up to order and associates.

Working with unique factorization domains makes it easier to analyze divisibility properties in rings.

In algebraic number theory, unique factorization rings often allow mathematicians to decompose elements uniquely into irreducible factors, simplifying many proofs.

A unique-headed bug was perched on the underside of the leaf, its tiny mouthparts probing for prey.

The researcher documented several unique-headed bugs discovered in the rainforest last summer.

Among all the paintings in the gallery, the curator declared Miko's abstract piece the uniquest, praising its unexpected harmony of color and texture.