Difference between revisions of "2000 PMWC Problems/Problem I4"
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If <math>A</math> and <math>B</math> are positive integers, then <math>B</math> must be the smallest positive integer that, when multiplied by <math>75600</math>, yields a perfect fourth power. The prime factorization of <math>75600</math> is <math>2^4 * 3^3 * 5^2 * 7^1</math>, so the smallest value of <math>B</math> is <math>2^0 * 3^1 * 5^2 * 7^3 = 25,725</math>. | If <math>A</math> and <math>B</math> are positive integers, then <math>B</math> must be the smallest positive integer that, when multiplied by <math>75600</math>, yields a perfect fourth power. The prime factorization of <math>75600</math> is <math>2^4 * 3^3 * 5^2 * 7^1</math>, so the smallest value of <math>B</math> is <math>2^0 * 3^1 * 5^2 * 7^3 = 25,725</math>. | ||
==See Also== | ==See Also== | ||
| + | Back to test: https://artofproblemsolving.com/wiki/index.php/2000_PMWC_Problems | ||
Latest revision as of 11:03, 23 December 2019
Problem
Given that 
. If 
and 
are positive integers, find the smallest value of .
Solution
If and are positive integers, then must be the smallest positive integer that, when multiplied by 
, yields a perfect fourth power. The prime factorization of is 
, so the smallest value of is 
.
See Also
Back to test: https://artofproblemsolving.com/wiki/index.php/2000_PMWC_Problems
