Pronađite par brojeva
za koji vrijedi:
predstavlja decimalni zapis broja. Npr. za
to bi bio broj
. Rezultat zapišite u obliku
.
Find a pair
such that
where
denotes the decimal representation of the number. For example, for
, this would be the number
.
Write the result in the form .
[lang=hr]
Pronađite par brojeva $a,b \in \mathbb{N}$ za koji vrijedi:
$$\gcd(a,b) = 1$$
$$\frac{a}{b} = b.a$$
$b.a$ predstavlja decimalni zapis broja. Npr. za $a=b=2$ to bi bio broj $2.2$.
Rezultat zapišite u obliku $1000 \cdot a + b$.
[/lang]
[lang=en]
Find a pair $a, b \in \mathbb{N}$ such that
\[
\gcd(a, b) = 1
\quad
and
\quad
\frac{a}{b} = b.a
\]
where $b.a$ denotes the decimal representation of the number.
For example, for $a = b = 2$, this would be the number $2.2$.
Write the result in the form $1000 \cdot a + b$.
[/lang]
