MathDB

4

Part of 2005 German National Olympiad

Problems(1)

Q(Q(Q(2005^2005)))=7

Source: DeMO 2005, classes 11 and 12/13, 2nd day, problem 4

5/10/2005
I am not a spammer, at least, this is the way I use to think about myself, and thus I will not open a new thread for the following problem from today's DeMO exam: Let Q(n) denote the sum of the digits of a positive integer n. Prove that Q(Q(Q(20052005)))=7Q\left(Q\left(Q\left(2005^{2005}\right)\right)\right)=7. [EDIT: Since this post was split into a new thread, I comment: The problem is completely analogous to the problem posted at http://www.mathlinks.ro/Forum/viewtopic.php?t=31409 , with the only difference that you have to consider the number 200520052005^{2005} instead of 444444444444^{4444}.] Darij
number theory unsolvednumber theory