Difference between revisions of "2023 SSMO Team Round Problems/Problem 13"
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Suppose <math>\sum_{k=2}^{\infty}G(k)</math> is <math>\frac{a+b\sqrt{c}}{d}</math>. Find the value of <math>a+b+c+d</math>. | Suppose <math>\sum_{k=2}^{\infty}G(k)</math> is <math>\frac{a+b\sqrt{c}}{d}</math>. Find the value of <math>a+b+c+d</math>. | ||
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==Solution== | ==Solution== | ||
Latest 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 
.
