Difference between revisions of "2023 SSMO Team Round Problems/Problem 13"
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Revision as of 22:25, 15 December 2023
Problem
Let denote the product of all divisors of Let denote the set of all integers that are both a multiple of and a factor of Let \[ -F(a) = \sqrt{\left|\log_{10}\left(\frac{D(10^{a})}{\prod_{\omega\in P(10^2,10^{a+2})}\omega}\right)\right|}\text{ and }G(n) = \sqrt[n-1]{\prod_{i=2}^{n}10^{F(i)}}. \] Suppose is . Find the value of .
Problem 14
Find the sum of all perfect squares of the form where and are positive integers such is prime and .