2000 PMWC Problems/Problem I4

Problem

Given that $A^4=75600\times B$ . If $A$ and $B$ are positive integers, find the smallest value of $B$ .

Solution

Given that $A^4=75600\times B$ . If $A$ and $B$ are positive integers, find the smallest value of $B$ .

If $A$ and $B$ are positive integers, then $B$ must be the smallest positive integer that, when multiplied by $75600$ , yields a perfect fourth power. The prime factorization of $75600$ is $2^4 * 3^3 * 5^2 * 7^1$ , so the smallest value of $B$ is $2^0 * 3^1 * 5^2 * 7^3 = 25,725$ .

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2000 PMWC Problems/Problem I4

Problem

Solution

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