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In a paper from 2004, the first author conjectured that such a permutation exists of Z/nZ, for all n except 2,3,5 and 7. Here we prove, as a special case of a more general result, that such a permutation exists for all n >= n_0, for some explcitly constructed number n_0 \\approx 1.4 x 10^{14}. We also construct such a permutation of Z/pZ for all primes p > 3 such that "},"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":"1506.05342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-17T14:33:52Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"25e47963b9b7acd1c8bbd332c8e66a69d7407680c1faa26a757d04f65d111615","abstract_canon_sha256":"44555308999f3874e90761b9bd9a8711801f5f887d37f6b09075ee67bd135c85"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:46:12.453106Z","signature_b64":"JmesBIiIOBrOxh+bxATKGtDnBC50W8vNREnomGOUcDhTsqYhy6C1t/jT2B1cJQyJwbqjlBGb8lyQRXtkH9UNAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0a3dbe39276c9cfb90eb3e28fe92d46e244de110f063014f7c748f4ba8e9245","last_reissued_at":"2026-05-18T01:46:12.452472Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:46:12.452472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Permutations destroying arithmetic progressions in finite cyclic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Anders Martinsson, Peter Hegarty","submitted_at":"2015-06-17T14:33:52Z","abstract_excerpt":"A permutation \\pi of an abelian group G is said to destroy arithmetic progressions (APs) if, whenever (a,b,c) is a non-trivial 3-term AP in G, that is c-b=b-a and a,b,c are not all equal, then (\\pi(a),\\pi(b),\\pi(c)) is not an AP. In a paper from 2004, the first author conjectured that such a permutation exists of Z/nZ, for all n except 2,3,5 and 7. Here we prove, as a special case of a more general result, that such a permutation exists for all n >= n_0, for some explcitly constructed number n_0 \\approx 1.4 x 10^{14}. 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