3 replies to this topic

[brhan]

The following puzzle is a variation of the question posted by bonanova.

I just found a number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 1.
When I divide it by 4, the remainder is 1.
When I divide it by 5, the remainder is 1.
When I divide it by 6, the remainder is 1.
When I divide it by 7, the remainder is 1.
When I divide it by 8, the remainder is 1.
When I divide it by 9, the remainder is 1.
When I divide it by 10, the remainder is 1.

But when I divide it by 11, the remainder is 0.

Can you find it?

[unreality]

Well obviously its a multiple of 11 and the number 1 beneath it is divisible by a bunch of numbers

[Writersblock]

I had to big time brute this one, but I got a few that work. <!-- s:mrgreen: --><!-- s:mrgreen: -->

Smallest.
25201
11*2291
10*2520+1
9*2800+1
8*3150+1
7*3600+1
6*4200+1
5,4,3 are just 10,8,6 *2
2 just has to be an odd number

Others
52921
80641
108361
136081
163801
191521
219241

I am guessing this is an infinite set

Edited to add a couple more numbers

[unreality]

I could write a computer program but it looks like ^ has already solved it