Square Free Factorization for the integers and beyond
... It then follows that x = i=1 αi yi is the unique square-free decomposition of x for which yn | yn−1 | · · · | y1 . Similar direct sum representations apply in any UFD - each entry corresponds to a particular prime element (working modulo associates), and indeed all the earlier arguments as well as t ...
... It then follows that x = i=1 αi yi is the unique square-free decomposition of x for which yn | yn−1 | · · · | y1 . Similar direct sum representations apply in any UFD - each entry corresponds to a particular prime element (working modulo associates), and indeed all the earlier arguments as well as t ...
CORE@TCA SIDE BY SIDE STANDARDS Algebra I/Algebra II
... 6. Add, subtract, multiply, and divide complex numbers 7. Add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions 8. Solve and graph quadratic equations by factoring, completing the square, or ...
... 6. Add, subtract, multiply, and divide complex numbers 7. Add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions 8. Solve and graph quadratic equations by factoring, completing the square, or ...
Pythagorean Triples
... but there is a sense in which it's \redundant": 2 3 4 5 = 6 8 10 . If a Pythagorean triple is not a proper multiple of of another triple, it is said to be primitive. Thus, x y z is a primitive Pythagorean triple if (x y z) = 1. The result I'll prove will show how you can generate all primiti ...
... but there is a sense in which it's \redundant": 2 3 4 5 = 6 8 10 . If a Pythagorean triple is not a proper multiple of of another triple, it is said to be primitive. Thus, x y z is a primitive Pythagorean triple if (x y z) = 1. The result I'll prove will show how you can generate all primiti ...
