2
votes
3answers
31 views

Show that $x_0$ must be an integer. Conclude that $\sqrt[n]{2}$ is irrational for every $n \geq 2$

I have a problem in my workbook that is as follows: Let $f = x^n + a_{n-1}x^{n-1}+\dots+a_1x+a_0 = 0 $ with $a_i \in \mathbb{Z}$. Suppose there exists a rational number $x_0$ with $f(x_0) = 0$. ...
6
votes
2answers
250 views

Prove that the function $f(x,y) = ax + by$ is onto

I have been thinking about this problem for a while and have gotten stuck. This is a homework question so I just require some hints to push me to the answer. Question: Let $a, b$ be integers. ...
1
vote
1answer
377 views

Formula To Determine Percentage Between Two Numbers After Certain Threshold

I have a formula I use to determine how opaque some validation text should be based upon the length of a user's input compared to the maximum lenth allowed. I want to modify it so that the "ramping ...
1
vote
1answer
155 views

Interesting prime factorization function divisibility problem [duplicate]

Possible Duplicate: Is the set of all numbers which divide a specific function of their prime factors, infinite? Let the function $f(n) =(p_1^{a+1}-1)(p_2^{b+1}-1)... $ where $n$ is an ...