A Combinatorial Proof of An Identity Involving Trigonometric Power Sums

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Rachanai Kaikeaw
Khanithar Naenudorn


Let gif.latex?n,m,d,r be integers where gif.latex?n,m,d&space;\geq&space;1. In this paper, we use a combinatorial proof to show that


by counting the number of solutions for the congruence gif.latex?x_1+x_2+\cdots+x_n\equiv&space;r\pmod{d} where gif.latex?1\leq&space;x_1,x_2,\ldots,x_n&space;\leq&space;m.

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Kaikeaw, R., & Naenudorn, K. (2022). A Combinatorial Proof of An Identity Involving Trigonometric Power Sums. Mathematical Journal by The Mathematical Association of Thailand Under The Patronage of His Majesty The King, 67(708), 25–39. Retrieved from https://ph02.tci-thaijo.org/index.php/MJMATh/article/view/245989
Research Article


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