Euler is Haunting

Number Theory Level 3

True or False?

$\quad$ If $n_1 > n_2$ are positive integers, then $\phi(n_1) > \phi(n_2)$ is satisfied.

Notation: $\phi(\cdot)$ denotes the Euler's totient function .

False, always True, always It is only sometimes true

1 solution

Chew-Seong Cheong
Mar 23, 2017

It depends on $n_1$ , $n_2$ , as shown below.

\[\begin{array} {} \phi(10) = 4 & \phi(11) = 10 & \phi(12) = 4 \\ \phi(13) = 12 & \phi(14) = 6 & \phi(15) = 8 \end{array} \]

Yes, It is correct, But sir Can we generalize this thing by not taking example and proving?

Md Zuhair - 4 years, 2 months ago

It doesn't worth the efforts.

Chew-Seong Cheong - 4 years, 2 months ago

Yes, Thats true

Md Zuhair - 4 years, 2 months ago

Sir, Dont you think that Cannot Be Said is a trolling option which deviates one from the real answer

Md Zuhair - 4 years, 2 months ago