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If the product of n positive real numbers is unity, then their sum is necessarily
a multiple of n
equal to n + 1/n
never less than n
a positive integer
Let the numbers be $$a_1,a_2....a_n.$$
Since the numbers are positive,
$$AM\geq GM$$
$$\frac{a_1+a_2+a_3....+a_n}{n}\geq (a_1*a_2....*a_n)^{1/n}$$
$$a_1+a_2+a_3....+a_n \geq n$$
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