1. The sum of four natural numbers is 2598. Determine the four natural numbers knowing that one of them is a prime number, and the other three numbers are consecutive.

Ionuţ Mazalu, Brăila
## Solution.

![](https://cdn.mathpix.com/cropped/2024_06_07_fcab45b555ec28e8536dg-2.jpg?height=226&width=1588&top_left_y=1024&top_left_x=236)
$3 \cdot a \vdots 3,2595 \vdots 3 \Rightarrow p \vdots 3, p$ prime $\Rightarrow p=3$
$3 \cdot a=2592 \Rightarrow a=864, a+1=865, a+2=866$ ..... $2p$