I am pretty sure that you have all seen already the 'famous' math trick where you take a triple digit number, write it down twice and then when you divide by 7,11,13 you get the three first digits back again! ( You will later see why that is. )

I prefer this version:

Take a triple digit number. ( e.g. 254 )

Write it down twice. ( here, 254254 )

The new number will always be divisible by 91.

If you don't believe me you can go ahead and try it out with as many numbers as you want, but it will always work. Here is the proof:

You have three digits, let's call them a,b,c. This means that:

They all have to be a part of !

So, our hypothesis is that:

n = 91 x k with k being a part of

since n is divisible by 91

( n is the six digit number )

Now here comes the 'tricky' part: You have to realize that you are working in a decimal system which means that our six digit number can be written like this:

You can factorize it to get this:

And we're done! Because:

So our earlier hypothesis was right. You can write any six digit number between 100100 and 999999 in this way:

n = 91 * k with k being a part of

Time for a little aparte. I just created this blog and any feedback and questions are much appreciated! I will continue to share any mathematical thingies I found interesting on here.