Mixed sums of squares and triangular numbers (II)

dc.creatorGuo, Song
dc.creatorPan, Hao
dc.creatorSun, Zhi-Wei
dc.date2005-05-10
dc.date2007-12-24
dc.date.accessioned2026-07-07T08:50:56Z
dc.date.available2026-07-07T08:50:56Z
dc.descriptionFor an integer $x$ let $t_x$ denote the triangular number $x(x+1)/2$. Following a recent work of Z. W. Sun, we show that every natural number can be written in any of the following forms with $x,y,z\in\Z$: $$x^2+3y^2+t_z, x^2+3t_y+t_z, x^2+6t_y+t_z, 3x^2+2t_y+t_z, 4x^2+2t_y+t_z.$$ This confirms a conjecture of Sun.
dc.identifierhttps://arxiv.org/abs/math/0505187
dc.identifierhttp://arxiv.org/abs/math/0505187
dc.identifierIntegers 7(2007), A56, 5 pp
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144772
dc.subjectNumber Theory
dc.subjectCombinatorics
dc.subject11E25; 11D85; 11P99
dc.titleMixed sums of squares and triangular numbers (II)
dc.typetext

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