Difference between revisions of "2019 Mock AMC 10B Problems/Problem 19"
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So plugging in <math>x=3, y=1</math>, and <math>n=2016</math>, we get <math>1+5+2-1 = 7</math> so the answer is <math>2^7 = \boxed{128}</math> | So plugging in <math>x=3, y=1</math>, and <math>n=2016</math>, we get <math>1+5+2-1 = 7</math> so the answer is <math>2^7 = \boxed{128}</math> | ||
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Revision as of 22:02, 3 October 2023
Problem
What is the largest power of that divides ?
Solution
.
By simple mod checking, we find that
, and .
Therefore, the largest powers of that divide each of these numbers are , and . The largest power of that divides is thus .
<baker77>
Solution 2
By LTE Lemma, we know that
So plugging in , and , we get so the answer is
<jayevvms123>