A relation between partitions and the number of divisors
... αm of X m if and only if n − i is a divisor of m. As i increases from 0 to n − 1, the number n − i decreases from n to 1. In this range there are d(m) numbers which divide m, so there are d(m) series (1 + X n−i + X 2(n−i) + . . .) for i = 0, ..., n − 1 which contribute +1 to αm . These contributions ...
... αm of X m if and only if n − i is a divisor of m. As i increases from 0 to n − 1, the number n − i decreases from n to 1. In this range there are d(m) numbers which divide m, so there are d(m) series (1 + X n−i + X 2(n−i) + . . .) for i = 0, ..., n − 1 which contribute +1 to αm . These contributions ...
File - Bowie Algebra 2
... You are probably familiar with finding the square and square root of a number. These two operations are inverses of each other. Similarly, there are roots that correspond to larger powers. ...
... You are probably familiar with finding the square and square root of a number. These two operations are inverses of each other. Similarly, there are roots that correspond to larger powers. ...
Full text
... Letting un-Fn, we have wn = Ln, where Ln is the nth Lucas number. Since 5 does not divide L0 = w0, we have established the well-known fact that no Ln is divisible by 5. On the contrary, if we let un = Zw, then wn = Ln+l + Ln_x. Here, all terms of wn are divisible by 5, since wY = 5. b) A consequence ...
... Letting un-Fn, we have wn = Ln, where Ln is the nth Lucas number. Since 5 does not divide L0 = w0, we have established the well-known fact that no Ln is divisible by 5. On the contrary, if we let un = Zw, then wn = Ln+l + Ln_x. Here, all terms of wn are divisible by 5, since wY = 5. b) A consequence ...
MATH 121 Course Outline - MJC - Curriculum Committee
... 1. Given a fourth degree polynomial with integer coefficients, use the Rational Roots Theorem, the Fundamental Theorem of Algebra, and synthetic division to find the complete factorization of the polynomial over the complex number system. 2. Graph a given rational function, citing details including ...
... 1. Given a fourth degree polynomial with integer coefficients, use the Rational Roots Theorem, the Fundamental Theorem of Algebra, and synthetic division to find the complete factorization of the polynomial over the complex number system. 2. Graph a given rational function, citing details including ...
