MathDB

1

Part of 2005 Federal Competition For Advanced Students, Part 2

Problems(2)

LCM(a,b,c) = a+b+c

Source: Austrian MO 2005 round 2

6/27/2005
Find all triples (a,b,c)(a,b,c) of natural numbers, such that LCM(a,b,c)=a+b+cLCM(a,b,c)=a+b+c
number theoryleast common multiplenumber theory unsolved
f(2x+1)=f(2x), f(3x+1)=f(3x), f(5x+1)=f(5x)

Source: Austrian MO 2005 round 2

6/27/2005
The function f:(0,...2005)→Nf : (0,...2005) \rightarrow N has the properties that f(2x+1)=f(2x)f(2x+1)=f(2x), f(3x+1)=f(3x)f(3x+1)=f(3x) and f(5x+1)=f(5x)f(5x+1)=f(5x) with x∈(0,1,2,...,2005)x \in (0,1,2,...,2005). How many different values can the function assume?
functioncombinatorics unsolvedcombinatorics