$f(x)=1988$ is too amazing!

Number Theory Level 1

We have a $f(x)=5x+9x+14x$ .

$f(x)=1988$ .

Can we express $x$ as $2^n$ such that $n$ is positive integer?

Yes No

1 solution

Matin Naseri
Aug 2, 2018

$5x+9x+14x{\implies}~(5+9+14)x = 28x$

$28x=1988, {\frac{1988}{28}={\boxed{71}}}$

$\therefore~$ $x~=~71$

$\boxed{71}$ can't be express as $2^n$ because $71$ is a prime number.

Hence the answer is $\color{#D61F06}{\boxed{No}}$ .