Fomin C.B.

Find 10 different natural numbers that have the property that their sum is divisible by each of them.
Note that the three numbers 1, 2, and 3 have the property that their sum is divisible by each of them. Now consider the numbers 1, 2, 3, and 6 ( $6=1+2+3$ ). Clearly, these four numbers have the same property. Now let's add a fifth number $1+2+3+6=12$, a sixth number $-1+2+3+6+12=24$, and so on. This way, we get the desired set of ten numbers $1,2,3,6,12,24,48,96,192,384$.

Send a comment