If an integer n has three unique prime divisors, then it follows that the largest prime divisor of n is less than or equal to cube root of n. true or false?

False

Step-by-step explanation:

Lets call the three prime divisors of n p, q, and r, being r the largest, we know:

Now, if

then

So:

Also, for every natural greater than one, we know:

so

from which:

So, we see, this means the preposition is false, we can find a particular counterexample:

q=2

p=3

p*q = 6

We need to choose a prime greater than 6

r=7

n= 2 * 3 *7 = 42

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step-by-step explanation:

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