relatively prime - 2

[logistic_guy]

Find all positive integers less than \(\displaystyle 11\) that are relatively prime to it.

 

[pka]

Find all positive integers less than \(\displaystyle 11\) that are relatively prime to it.

The answer here depends on the textbook definition of relatively prime!
Here is the most common: two positive integers [imath]a\ \&\ b[/imath] are said to be relatively if [imath]\gcd(a,b)=1[/imath].
Note that [imath]11[/imath] has only two divisors: [imath]1\ \&\ 11[/imath].

 

[logistic_guy]

The answer here depends on the textbook definition of relatively prime!
Here is the most common: two positive integers [imath]a\ \&\ b[/imath] are said to be relatively if [imath]\gcd(a,b)=1[/imath].
Note that [imath]11[/imath] has only two divisors: [imath]1\ \&\ 11[/imath].

This means that the numbers \(\displaystyle \textcolor{blue}{1}\), \(\displaystyle \textcolor{blue}{2}\), \(\displaystyle \textcolor{blue}{3}\), \(\displaystyle \textcolor{blue}{4}\), \(\displaystyle \textcolor{blue}{5}\), \(\displaystyle \textcolor{blue}{6}\), \(\displaystyle \textcolor{blue}{7}\), \(\displaystyle \textcolor{blue}{8}\), \(\displaystyle \textcolor{blue}{9}\), and \(\displaystyle \textcolor{blue}{10}\) are all relatively prime to the number \(\displaystyle \textcolor{red}{11}\).

Shocking result

 

[pka]

This means that the numbers \(\displaystyle \textcolor{blue}{1}\), \(\displaystyle \textcolor{blue}{2}\), \(\displaystyle \textcolor{blue}{3}\), \(\displaystyle \textcolor{blue}{4}\), \(\displaystyle \textcolor{blue}{5}\), \(\displaystyle \textcolor{blue}{6}\), \(\displaystyle \textcolor{blue}{7}\), \(\displaystyle \textcolor{blue}{8}\), \(\displaystyle \textcolor{blue}{9}\), and \(\displaystyle \textcolor{blue}{10}\) are all relatively prime to the number \(\displaystyle \textcolor{red}{11}\).
Shocking result

Indeed

 

[logistic_guy]

Indeed