Find the largest number obtainable as the product of positive integers
whose sum is 1976.

Question

Find the largest number obtainable as the product of positive integers
whose sum is 1976.

parthkohli · Answer

Is this a brilliant.org question?

anonymous · Answer

no its not

anonymous · Answer

is it a problem to ask brilliant.org questions on OS

parthkohli · Answer

I guess it'd be $988 \times 988$.

anonymous · Answer

let $$x_1,x_2,....,x_n \space be \space the  \space integers $$
$$AM \ge GM$$
$$\huge \frac{x_1+x_2+...+x_n}{n} \ge \sqrt[n]{x_1x_2...x_n}$$
$$\huge \frac{1976^n}{n} \ge x_1x_2...x_n$$

parthkohli · Answer

When you want to find the highest such number, just halve the sum.

anonymous · Answer

denominator n^n

parthkohli · Answer

Oh myy...

anonymous · Answer

wats the problem

parthkohli · Answer

I am not too good at all those applications . . . I just know that the numbers are $988$ and $988$

anonymous · Answer

okay i will post the solution but its so much of analysis

anonymous · Answer

attachment