Full text
... In this paper we show that for every n there are infinitely many n~gonal numbers that can be written as the product of two other n-gonal numbers, and in fact show how to generate infinitely many such products. We suspect that our method does not generate all of the solutions for every n, but we have ...
... In this paper we show that for every n there are infinitely many n~gonal numbers that can be written as the product of two other n-gonal numbers, and in fact show how to generate infinitely many such products. We suspect that our method does not generate all of the solutions for every n, but we have ...
Math for Developers
... Any non-prime integer can be presented as product of primes Examples: 6 = 2 x 3, 24 = 2 x 2 x 2 x 3, 95 = 5 x 19 Non-prime numbers are called composite numbers ...
... Any non-prime integer can be presented as product of primes Examples: 6 = 2 x 3, 24 = 2 x 2 x 2 x 3, 95 = 5 x 19 Non-prime numbers are called composite numbers ...
2016 UI UNDERGRADUATE MATH CONTEST Solutions
... 6. Suppose a1 , a2 , a3 , . . . is a sequence of positive integers such that an+1 is obtained from an by attaching an arbitrary digit except 9 to the right of an . (Examples of such sequences are 1, 11, 113, 1131, 11317, 113173, . . . and 2, 20, 201, 2014, 20148, 201483, . . . .) Prove that any suc ...
... 6. Suppose a1 , a2 , a3 , . . . is a sequence of positive integers such that an+1 is obtained from an by attaching an arbitrary digit except 9 to the right of an . (Examples of such sequences are 1, 11, 113, 1131, 11317, 113173, . . . and 2, 20, 201, 2014, 20148, 201483, . . . .) Prove that any suc ...
Ch. 1.1 PowerPoint
... You can then use the number line to start at negative 12 and go left 19 units because you are adding a negative number. ...
... You can then use the number line to start at negative 12 and go left 19 units because you are adding a negative number. ...
HW 7. - U.I.U.C. Math
... It is not particularly difficult, it is not hard to guess a formula for magic number, and proving that this number has the desired “magic” properties is not that hard either. #1 A magic matrix. Consider the n × n matrix obtained by filling the rows of this matrix with the numbers 1, 2, . . . , n2 , ...
... It is not particularly difficult, it is not hard to guess a formula for magic number, and proving that this number has the desired “magic” properties is not that hard either. #1 A magic matrix. Consider the n × n matrix obtained by filling the rows of this matrix with the numbers 1, 2, . . . , n2 , ...
real numbers, intervals, and inequalities
... By convention, infinite intervals of the form [a, +⬁) or (−⬁, b] are considered to be closed because they contain their endpoint, and intervals of the form (a, +⬁) and (−⬁, b) are considered to be open because they do not include their endpoint. The interval (−⬁, +⬁), which is the set of all real num ...
... By convention, infinite intervals of the form [a, +⬁) or (−⬁, b] are considered to be closed because they contain their endpoint, and intervals of the form (a, +⬁) and (−⬁, b) are considered to be open because they do not include their endpoint. The interval (−⬁, +⬁), which is the set of all real num ...
Estimating With Square Roots
... Estimating Square Roots Worksheet – Homework 1. What are the two whole numbers closest to ...
... Estimating Square Roots Worksheet – Homework 1. What are the two whole numbers closest to ...
TRANSCENDENTAL NUMBERS
... Three of the oldest problems in mathematics The theory of algebraic and transcendental numbers has enabled mathematicians to settle three well-known geometric problems that have come down from antiquity. These problems come from classical Greek geometry. According to Plato the only ”perfect” geometr ...
... Three of the oldest problems in mathematics The theory of algebraic and transcendental numbers has enabled mathematicians to settle three well-known geometric problems that have come down from antiquity. These problems come from classical Greek geometry. According to Plato the only ”perfect” geometr ...