Stark, H. M. An introduction to number theory (Markham Mathematics Series). (English) Zbl 0198.06401 Chicago: Markham Publishing Company X, 347 p. (1970). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 20 Documents Keywords:number theory PDFBibTeX XML Online Encyclopedia of Integer Sequences: Represent the ring of Eisenstein integers E = {x+y*omega: x, y rational integers, omega = exp(2*Pi*i/3)} by the cells of a hexagonal grid; number the cells of the grid along a counterclockwise hexagonal spiral, with the cells 0, 1 numbered 0, 1. Sequence lists the index numbers of the cells which are 0 or a prime in E. Represent the ring of Gaussian integers E = {x+y*i: x, y rational integers, i = sqrt(-1)} by the cells of a square grid; number the cells of the grid along a counterclockwise square spiral, with the cells representing the ring identities 0, 1 numbered 0, 1. Sequence lists the index numbers of the cells which are 0 or a prime in E. Represent the ring R = {x+y*sqrt(-2): x, y rational integers} by the cells centered at the points (x,y) of a square grid; number the cells of the grid along a counterclockwise square spiral, with the cells at (0,0) and (1,0) numbered 0, 1. Sequence lists the index numbers of the cells which are 0 or a prime in R. Use the cells of a hexagonal grid to represent the algebraic integers in the integer ring of Q(sqrt(-7)), as explained in the comments. Number the cells along the counterclockwise hexagonal spiral that starts with cells 0 and 1 representing integers 0 and 1. List the cells that represent 0 or a prime in the ring. Use the cells of a hexagonal grid to represent the algebraic integers in the integer ring of Q(sqrt(-11)) as explained in the comments. Number the cells along the counterclockwise hexagonal spiral that starts with cells 0 and 1 representing integers 0 and 1. List the cells that represent 0 or a prime in the ring. Use the cells of a hexagonal grid to represent the algebraic integers in the integer ring of Q(sqrt(-19)) as explained in the comments. Number the cells along the counterclockwise hexagonal spiral that starts with cells 0 and 1 representing integers 0 and 1. List the cells that represent 0 or a prime in the ring. Use the cells of a hexagonal grid to represent the algebraic integers in the integer ring of Q(sqrt(-43)) as explained in the comments. Number the cells along the counterclockwise hexagonal spiral that starts with cells 0 and 1 representing integers 0 and 1. List the cells that represent 0 or a prime in the ring. Use the cells of a hexagonal grid to represent the algebraic integers in the integer ring of Q(sqrt(-67)) as explained in the comments. Number the cells along the counterclockwise hexagonal spiral that starts with cells 0 and 1 representing integers 0 and 1. List the cells that represent 0 or a prime in the ring. Use the cells of a hexagonal grid to represent the algebraic integers in the integer ring of Q(sqrt(-163)) as explained in the comments. Number the cells along the counterclockwise hexagonal spiral that starts with cells 0 and 1 representing integers 0 and 1. List the cells that represent 0 or a prime in the ring.