MathDB

1

Part of 2012 Junior Balkan Team Selection Tests - Moldova

Problems(2)

minimum of a*b*c+d*e*f+g*h*k

Source:

3/5/2012
Let 1≤a,b,c,d,e,f,g,h,k≤9 1\leq a,b,c,d,e,f,g,h,k \leq 9 and a,b,c,d,e,f,g,h,k a,b,c,d,e,f,g,h,k are different integers, find the minimum value of the expression E=a∗b∗c+d∗e∗f+g∗h∗k E = a*b*c+d*e*f+g*h*k and prove that it is minimum.
inequalitiesinequalities unsolved
Sum and Product of sequence

Source:

8/9/2012
Find a sequence of 2012 2012 distinct integers bigger than 0 0 such that their sum is a perfect square and their product is a perfect cube.
number theory proposednumber theory