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We prove that $f$ is a permutation polynomial of $\\Bbb F_{q^2}$ if and only if one of the following occurs: (i) $q$ is even and $\\text{Tr}_{q/2}(\\frac 1t)=0$; (ii) $q\\equiv 1\\pmod 8$ and $t^2=-2$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1303.0568","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-03T21:02:17Z","cross_cats_sorted":[],"title_canon_sha256":"f09615e522de9a98e2dfbf5ab81d32f06c51229aa15b2fb50832b4042989be30","abstract_canon_sha256":"6bd0a5de0d4ac5c925b87e010294f5248eeb2c61a3ddbec579eb9b6579900236"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:55.565427Z","signature_b64":"HLw2VpLzhhyM1nQads8mN8ZvqNn7f5cAbWq3Wu1BmiN9g4c8xsjbMdDQqFfaaO674bhjDj9MsvsGZvf+mKz5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8c398f4c68af81cfa43eba9f17eefa377b8b8e8bc6c415dcb5a0dcf210315ce","last_reissued_at":"2026-05-18T03:31:55.564685Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:55.564685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Class of Permutation Trinomials over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Xiang-dong Hou","submitted_at":"2013-03-03T21:02:17Z","abstract_excerpt":"Let $q>2$ be a prime power and $f=-{\\tt x}+t{\\tt x}^q+{\\tt x}^{2q-1}$, where $t\\in\\Bbb F_q^*$. 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