{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-26T00:16:20.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-05-26T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":46681,"title":"Determine the kth Primitive Root of Unity","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDetermine all prime numbers less than n (input) that have a kth (k\u0026lt;prime number) root of unity modulo (prime number) and determine the primitive kth root of unity for each of those prime numbers (modulo those prime numbers).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [prime_numbers, primitive_roots] = primitiveKthRootofUnity(n,k)\r\n prime_numbers=primes(n);\r\n primitive_roots=prime_numbers;\r\nend","test_suite":"%%\r\nn=100000;\r\nk=1024;\r\np=[12289,13313,15361,18433,19457,25601,37889,39937,40961,50177,58369,59393,61441,64513,65537,70657,76801,79873,80897,83969,86017,87041,95233];\r\nr=[49,7,84,159,5,31,95,143,40,35,29,9,21,156,431,53,231,230,6,329,82,30,223];\r\n[prime_numbers, primitive_roots] = primitiveKthRootofUnity(n,k)\r\nassert(isequal(prime_numbers,p))\r\nassert(isequal(primitive_roots,r))\r\n%%\r\nn=10000;\r\nk=256;\r\np=[257,769,3329,7681,7937,9473];\r\nr=[3,7,17,198,71,88];\r\n[prime_numbers, primitive_roots] = primitiveKthRootofUnity(n,k)\r\nassert(isequal(prime_numbers,p))\r\nassert(isequal(primitive_roots,r))\r\n%%\r\nn=10000;\r\nk=210;\r\np=[211,421,631,1051,1471,2311,2521,2731,3361,3571,4201,4621,4831,5881,6091,6301,7351,7561,8191,8821,9241,9661,9871];\r\nr=[2,4,27,3,12,135,39,46,38,139,9,99,96,51,17,152,86,118,46,215,184,148,181];\r\n[prime_numbers, primitive_roots] = primitiveKthRootofUnity(n,k)\r\nassert(isequal(prime_numbers,p))\r\nassert(isequal(primitive_roots,r))\r\n    ","published":true,"deleted":false,"likes_count":1,"comments_count":8,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-06T02:04:32.000Z","updated_at":"2026-05-30T17:05:06.000Z","published_at":"2020-10-06T02:04:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine all prime numbers less than n (input) that have a kth (k\u0026lt;prime number) root of unity modulo (prime number) and determine the primitive kth root of unity for each of those prime numbers (modulo those prime numbers).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"problems":[{"id":46681,"title":"Determine the kth Primitive Root of Unity","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eDetermine all prime numbers less than n (input) that have a kth (k\u0026lt;prime number) root of unity modulo (prime number) and determine the primitive kth root of unity for each of those prime numbers (modulo those prime numbers).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [prime_numbers, primitive_roots] = primitiveKthRootofUnity(n,k)\r\n prime_numbers=primes(n);\r\n primitive_roots=prime_numbers;\r\nend","test_suite":"%%\r\nn=100000;\r\nk=1024;\r\np=[12289,13313,15361,18433,19457,25601,37889,39937,40961,50177,58369,59393,61441,64513,65537,70657,76801,79873,80897,83969,86017,87041,95233];\r\nr=[49,7,84,159,5,31,95,143,40,35,29,9,21,156,431,53,231,230,6,329,82,30,223];\r\n[prime_numbers, primitive_roots] = primitiveKthRootofUnity(n,k)\r\nassert(isequal(prime_numbers,p))\r\nassert(isequal(primitive_roots,r))\r\n%%\r\nn=10000;\r\nk=256;\r\np=[257,769,3329,7681,7937,9473];\r\nr=[3,7,17,198,71,88];\r\n[prime_numbers, primitive_roots] = primitiveKthRootofUnity(n,k)\r\nassert(isequal(prime_numbers,p))\r\nassert(isequal(primitive_roots,r))\r\n%%\r\nn=10000;\r\nk=210;\r\np=[211,421,631,1051,1471,2311,2521,2731,3361,3571,4201,4621,4831,5881,6091,6301,7351,7561,8191,8821,9241,9661,9871];\r\nr=[2,4,27,3,12,135,39,46,38,139,9,99,96,51,17,152,86,118,46,215,184,148,181];\r\n[prime_numbers, primitive_roots] = primitiveKthRootofUnity(n,k)\r\nassert(isequal(prime_numbers,p))\r\nassert(isequal(primitive_roots,r))\r\n    ","published":true,"deleted":false,"likes_count":1,"comments_count":8,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-06T02:04:32.000Z","updated_at":"2026-05-30T17:05:06.000Z","published_at":"2020-10-06T02:04:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine all prime numbers less than n (input) that have a kth (k\u0026lt;prime number) root of unity modulo (prime number) and determine the primitive kth root of unity for each of those prime numbers (modulo those prime numbers).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"errors":[],"facets":[[],[{"value":"medium","count":1,"selected":false}]],"term":"tag:\"root-of-unity\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}