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2k is a perfect square, 3k is a perfect cube, and 5k is a perfect 4th power. What is the sum of the exponents in the prime factorization of the smallest such positive integer k ?

 Jun 20, 2021
 #1
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I think no such k exists.

 Jun 20, 2021
 #2
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The immage below is simmilar question...The different between the two question > "5k is a perfect 4th power." and your question "5k is a perfect 5th power."

Ref:  https://web2.0calc.com/questions/plz-help-fast-urgent

 

 Jun 20, 2021
 #3
avatar+287 
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Exactly my point.   Changing 5th to 4th makes it impossible.   I can show it's impossible but I'll leave you to see it for yourself.   I've solved and posted a solution for 5th already.

 Jun 21, 2021

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