{"paper":{"title":"A note on the high power Diophantine equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Farzali Izadi, Mehdi Baghalaghdam","submitted_at":"2017-05-11T18:02:48Z","abstract_excerpt":"In this paper, we solve the simultaneous Diophantine equations(SDE) x_1^u+...+x_n^u=k(y_1^u+...+y_{n/k}); u=1,3, where n >3, and k< n, is a divisor of n , and obtain nontrivial parametric solution for them. Furthermore we present a method for producing another solution for the above Diophantine equation (DE) for the case u = 3, when a solution is given. We work out some examples and find nontrivial parametric solutions for each case in nonzero integers. Also we prove that the other DE p_1x_1^{a_1}+....+p_nx_n^{a_n}=q_1y_1^{b_1}+...+q_my_m^{b_m} , has parametric solution and infinitely many sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04338","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}