# Help to solve this please ? integer problem

## Main Question or Discussion Point

we must obtain 'N' and a(i) i=1,2,3,.............,N on condition that

the product $$a(1)a(2)a(3)..........a(N)$$ is the highest possible

$$a(1)+a(2)+a(3)+........+a(N)=73$$

every a(i) is positive

here N (this is the hardest part) is not known and must be calculated

Well, since $3^{1/3}>2^{1/2}=4^{1/4}$, I'd suggest using as many 3s as will fit, making the rest a 2 or 4. In this case twenty three 3s and one 4 would seem to be the best. Now just check my work and make sure I didn't miss something silly.