5
votes
3answers
359 views

Roots of functions / polynomials

Please excuse the naivity of this question, but it is a concept that I just have not been able to grasp entirely. My question is, why are the roots of a function, or a system of polynomials so ...
3
votes
2answers
58 views

If $x\in\mathbb R$, solve $x^{\lfloor x\rfloor}=\frac{9}{2}$, where $\lfloor x\rfloor$ is the integer part of $x$.

If $x\in\mathbb R$, solve $x^{\lfloor x\rfloor}=\frac{9}{2}$, where $\lfloor x\rfloor$ is the integer part of $x$. Of course, $x=\lfloor x\rfloor+\{x\}$, where $\{x\}$ is the fractional part of ...
3
votes
1answer
40 views

Why is the RSA exponentiation function a permutation (i.e. a bijection) over $\mathbb{Z}^*_N$

Why is the RSA exponentiation function a permutation (i.e. a bijection) over $\mathbb{Z}^*_N$? My doubt was specifically why, when raising to the power of the decryption key d we get a unique number ...
4
votes
3answers
177 views

If $x\in\mathbb R$, solve $4x^2-40\lfloor x\rfloor+51=0$.

If $x\in\mathbb R$, solve $$4x^2-40\lfloor x\rfloor+51=0$$ where $\lfloor x\rfloor$ denotes the integer part of the number. $\lfloor x\rfloor\le x$ and $\lfloor x\rfloor=x-\{x\}$, where $\{x\}$ ...
6
votes
2answers
135 views

Prove that $\sqrt[2012]{2012!}<\sqrt[2013]{2013!}$

I need to prove that $\sqrt[2012]{2012!}<\sqrt[2013]{2013!}$ My attempt: Let $a=\sqrt[2012]{2012!}$ and $b=\sqrt[2013]{2013!}$ Then $\displaystyle\frac{b^{2012}}{a^{2012}}=\frac{2013}{b}$ ...
3
votes
2answers
130 views

How to find the roots of $f(x)=x^{2}+2x+2$ in $\mathbb{Z}_{3}$ ? in $\mathbb{Z}_{5}$ ? in $\mathbb{R}$?

Normally I just guess a root and then smash one out in high degree functions, or complete squares or any other number of mathemagical tricks, but my textbook has decided to break numbers on me and I ...
0
votes
1answer
213 views

Number theory - Primitive root of $338$ [closed]

Im having problem $338$ root. I know it has a root because $13^2\times2=338$ but what is the correct way to find it??
1
vote
2answers
88 views

Find $y=\sqrt{x}$ where $x$ and $y$ positive integers in polynomial time?

Let $x$ be a positive integer and let $y$ be a real number such that $$y=\sqrt{x}$$ Objectives: If $y$ is an integer, find it in polynomial time. If $y$ is not an integer, prove that there is no ...
2
votes
2answers
137 views

Solving polynomials in $\mathbb{Q}[X]$ exactly

I wanted to write an equation solver for rational polynomials in one variable $X$. However, such solutions do not need to be in $\mathbb{Q}$. What I wanted was to display solutions "lossless", i.e. ...
1
vote
2answers
235 views

Need help with this primitive roots question

Question: If p and q are odd primes and $({a^p+1})/q$, show that either $(a+1)/q$ or $ q= 2kp + 1$ for some integer $k$ I read the theorem that says If p and q are odd primes and $({a^p-1})/q$, show ...