This number theoretic problem motivated by T-6(Team competition) ARML 2009. There are an infinite number of positive integers whose odd divisors sum to 400. They are exactly of the form (2^k(7))^3 until proven otherwise.
PHD mathematician Vishnu Thakkar carefully and clearly explained why summing and multiplying all the finite geometric series, excluding the prime number 2 as a common ratio, gives the sum of the odd natural number divisors/factors of an integer with a known prime factorization.
I think 2744=14^3 is the unique integer satisfying the 3 conditions, but did not rigorously show this to be so.
The venues for this high school math event/competition are Penn State, University of Iowa, University of Alabama in Huntsville, and the University of Nevada, Reno.
Негізгі бет Let n ∈ N be a cubed integer with 16 divisors, and odd positive divisors sum to 400. Find n
Пікірлер: 3