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Klauber's 1932 paper describes a triangle in which row n contains the numbers (n − 1) 2 + 1 through n 2. As in the Ulam spiral, quadratic polynomials generate numbers that lie in straight lines. Vertical lines correspond to numbers of the form k 2 − k + M. Vertical and diagonal lines with a high density of prime numbers are evident in the ...
This is the "grid" or "boxes" structure which gives the multiplication method its name. Faced with a slightly larger multiplication, such as 34 × 13, pupils may initially be encouraged to also break this into tens. So, expanding 34 as 10 + 10 + 10 + 4 and 13 as 10 + 3, the product 34 × 13 might be represented:
An economical number has been defined as a frugal number, but also as a number that is either frugal or equidigital. gcd( m , n ) ( greatest common divisor of m and n ) is the product of all prime factors which are both in m and n (with the smallest multiplicity for m and n ).
The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which n/m is again an integer (which is necessarily also a divisor of n). For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21). If m is a divisor of n, then so is −m. The tables below only ...
As in Sudoku, the goal of each puzzle is to fill a grid with digits –– 1 through 4 for a 4×4 grid, 1 through 5 for a 5×5, 1 through 6 for a 6×6, etc. –– so that no digit appears more than once in any row or any column (a Latin square). Grids range in size from 3×3 to 9×9.
A set of 20 points in a 10 × 10 grid, with no three points in a line. The no-three-in-line problem in discrete geometry asks how many points can be placed in the n × n {\displaystyle n\times n} grid so that no three points lie on the same line.
The next number in the direction of the arrow is 4. So think of the next number after 7 that ends with 4, which is 14. The next number in the direction of the arrow is 1. So think of the next number after 14 that ends with 1, which is 21. After coming to the top of this column, start with the bottom of the next column, and travel in the same ...
The palindromic prime 10 150006 + 7 426 247 × 10 75 000 + 1 is a 10-happy prime with 150 007 digits because the many 0s do not contribute to the sum of squared digits, and 1 2 + 7 2 + 4 2 + 2 2 + 6 2 + 2 2 + 4 2 + 7 2 + 1 2 = 176, which is a 10-happy number. Paul Jobling discovered the prime in 2005. [10]