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On Graham partitions twisted by the Legendre symbol
Open Mathematics ( IF 1.7 ) Pub Date : 2023-10-26 , DOI: 10.1515/math-2023-0134 Byungchan Kim 1 , Ji Young Kim 2 , Chong Gyu Lee 3 , Sang June Lee 4 , Poo-Sung Park 5 , Yoon Kyung Park 1
Open Mathematics ( IF 1.7 ) Pub Date : 2023-10-26 , DOI: 10.1515/math-2023-0134 Byungchan Kim 1 , Ji Young Kim 2 , Chong Gyu Lee 3 , Sang June Lee 4 , Poo-Sung Park 5 , Yoon Kyung Park 1
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We investigate when there is a partition of a positive integer n n , n = f ( λ 1 ) + f ( λ 2 ) + ⋯ + f ( λ ℓ ) , n=f\left({\lambda }_{1})+f\left({\lambda }_{2})+\cdots +f\left({\lambda }_{\ell }), satisfying that 1 = χ p ( λ 1 ) λ 1 + χ p ( λ 2 ) λ 2 + ⋯ + χ p ( λ ℓ ) λ ℓ , 1=\frac{{\chi }_{p}\left({\lambda }_{1})}{{\lambda }_{1}}+\frac{{\chi }_{p}\left({\lambda }_{2})}{{\lambda }_{2}}+\cdots +\frac{{\chi }_{p}\left({\lambda }_{\ell })}{{\lambda }_{\ell }}, where χ p {\chi }_{p} is the Legendre symbol modulo prime p p and f ( k ) = k f\left(k)=k or the k k th m m -gonal number with m = 3 m=3 , 4, or 5.
更新日期：2023-10-26
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