Number theory · Divisor function · Sum of divisors · Digit sum · Congruences
Determine all natural numbers \(n\) with all of the following properties:
\(n\) is divisible by \(2\) but not by \(4\); the sum of the digits of \(n\) equals \(6\); the number of divisors of \(n\) equals \(8\); the sum of the divisors of \(n\) is divisible by \(10\); and \(n\) leaves neither remainder \(12\) nor remainder \(14\) on division by \(16\).
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Serbian Regional Competition 2017, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source