Homework Statement
If a^2 divides b^2, then a divides b
Also
If a^2 divides b^3, then a divides b
Homework EquationsThe Attempt at a Solution
For the first question, if a^2 divides b^2, then b^2=(a^2)c where c is some integer
c=(b^2)/(a^2)
c=(b/a)^2
The answers in the back say that it is...
Homework Statement
Let n be an integer. Prove that the integers 6n-1, 6n+1, 6n+2, 6n+3, and 6n+5 are pairwise relatively prime.
Homework EquationsThe Attempt at a Solution
I tried to prove that the first two integers in the list are relatively prime.
(6n-1)-(6n+1)=1 (trying to eliminate...
Homework Statement
Find the least squares approximation of cos^3(x) by a combination of sin(x) and cos(x) over the interval (0, 2pi)
Homework EquationsThe Attempt at a Solution
I know how to find a least squares approximation with vectors, but I don't even know how to start with a function...