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Let $r$ be a prime divisor of $q-1$ such that the largest prime power part of $q-1$ has the form $r^s$. Then there is a constant $0<\\epsilon<1$ such that for a ratio at least $ {q^{-\\epsilon h}}$ of $\\alpha\\in \\mathbb{F}_{q^{h}} \\backslash\\mathbb{F}_{q}$, the set $S=\\{ \\alpha-x^t, x\\in\\mathbb{F}_{q}\\}$ of cardinality $1+\\frac {q-1} {M(h)}$ contains a non-d-th power i","authors_text":"Jiyou Li","cross_cats":["cs.CC","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-20T14:43:26Z","title":"On the construction of small subsets containing special elements in a finite field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05976","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c81e9c0ccc5472087ebfc872b1750224fc0a4414f8e7b9291515626693d21d18","target":"record","created_at":"2026-05-18T00:36:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"632d18b773f2e47fbf5993a05476de8326a603214541181bdb22f0b3c1d6612b","cross_cats_sorted":["cs.CC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-20T14:43:26Z","title_canon_sha256":"4a2735aadcfce6c10711e48591ed62e13df77db0472a2d47831473ff6f32d702"},"schema_version":"1.0","source":{"id":"1708.05976","kind":"arxiv","version":2}},"canonical_sha256":"7d15152f0a368613ae2eead056e3422c0f1b349dd0605a4d6e3ab0b6ca2eb662","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d15152f0a368613ae2eead056e3422c0f1b349dd0605a4d6e3ab0b6ca2eb662","first_computed_at":"2026-05-18T00:36:02.660146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:02.660146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MmbhlYOK42Dd6YxJIdKmMNlqiiTs87HbIGRJPof23Mpg4tUt943ii8RH1Mc/cBtrOGWZ1D1SqsDM3peez767Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:02.660511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.05976","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c81e9c0ccc5472087ebfc872b1750224fc0a4414f8e7b9291515626693d21d18","sha256:0b51147545fe1c971da9912c331332b0d947d372306f93b74c7eb81fa5cff483"],"state_sha256":"6b68a50ee25304926c1f881727be343ed6eead357f3b6624c18b43f3e70ef02b"}