If we divide a number by 4, the remainder is 3; if we divide it by 9, the remainder is 5. What is the remainder when we divide it by 36?
The sought number: $n=36 x+r$ can be written in the form where $r<36$ and $x$ is any ordinary integer.

The remainder $r$, when divided by 4, gives a remainder of 3, and when divided by 9, gives a remainder of 5, if $n$ has these properties; if $r$ has these properties, then $n$ also has them. Therefore, it is sufficient to determine the value of $r$ such that

$$
r=4 a+3=9 b+5<35
$$

thus, $b<3$. The number $r=4 a+3$ is odd; it is necessary that $9 b+5$ is also odd, so $b$ must be even. According to this, only $b=2$ fits, and thus $r=23$ 円

Baán Sándor (Bencés g. VI. o. Kószeg)[^0]


[^0]:    ${ }^{1}$ Form the product of the numbers less than 36 that are of the form $4 a+3$; among these, only 23 is the number that gives a remainder of 5 when divided by 9.