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Full-Text Articles in Discrete Mathematics and Combinatorics
A Proof Of The "Magicness" Of The Siam Construction Of A Magic Square, Joshua Arroyo
A Proof Of The "Magicness" Of The Siam Construction Of A Magic Square, Joshua Arroyo
Rose-Hulman Undergraduate Mathematics Journal
A magic square is an n x n array filled with n2 distinct positive integers 1, 2, ..., n2 such that the sum of the n integers in each row, column, and each of the main diagonals are the same. A Latin square is an n x n array consisting of n distinct symbols such that each symbol appears exactly once in each row and column of the square. Many articles dealing with the construction of magic squares introduce the Siam method as a "simple'' construction for magic squares. Rarely, however, does the article actually prove that the …
On Orders Of Elliptic Curves Over Finite Fields, Yujin H. Kim, Jackson Bahr, Eric Neyman, Gregory Taylor
On Orders Of Elliptic Curves Over Finite Fields, Yujin H. Kim, Jackson Bahr, Eric Neyman, Gregory Taylor
Rose-Hulman Undergraduate Mathematics Journal
In this work, we completely characterize by $j$-invariant the number of orders of elliptic curves over all finite fields $F_{p^r}$ using combinatorial arguments and elementary number theory. Whenever possible, we state and prove exactly which orders can be taken on.