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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.13645 |
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| _version_ | 1866912490556751872 |
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| author | Bulkhali, Nasser Abdo Saeed Vanitha, A. Chaudhary, M. P. |
| author_facet | Bulkhali, Nasser Abdo Saeed Vanitha, A. Chaudhary, M. P. |
| contents | Generalized $m$-gonal numbers are those $p_m(x)= [ (m - 2)x^2 - (m - 4)x ]/2 $ where $x$ and $m$ are integers with $m \geq 3$. If any nonnegative integer can be written in the form $ap_r(h)+bp_s(l)+cp_t(m)+dp_u(n)$, where $a,b,c,d$ are positive integers, then we call $ap_r(h)+bp_s(l)+cp_t(m)+dp_u(n)$ a universal quaternary sum. In this paper, we determine the universality of many quaternary sums when $r,s,t,u \in \{3,4,5,8\}$, using the theory of Ramanujan's theta function identities |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13645 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Bulkhali, Nasser Abdo Saeed Vanitha, A. Chaudhary, M. P. Number Theory 11D72, 11E20, 11E25, 11F27, 14H42 Generalized $m$-gonal numbers are those $p_m(x)= [ (m - 2)x^2 - (m - 4)x ]/2 $ where $x$ and $m$ are integers with $m \geq 3$. If any nonnegative integer can be written in the form $ap_r(h)+bp_s(l)+cp_t(m)+dp_u(n)$, where $a,b,c,d$ are positive integers, then we call $ap_r(h)+bp_s(l)+cp_t(m)+dp_u(n)$ a universal quaternary sum. In this paper, we determine the universality of many quaternary sums when $r,s,t,u \in \{3,4,5,8\}$, using the theory of Ramanujan's theta function identities |
| title | Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions |
| topic | Number Theory 11D72, 11E20, 11E25, 11F27, 14H42 |
| url | https://arxiv.org/abs/2507.13645 |