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Find the number of positive integers ${}n$ that satisfy $\lfloor \sqrt{n} \rfloor + \lfloor \sqrt{4n} \rfloor = 5.$

 Sep 8, 2023
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No positive integer n makes this true...

 

If n = 3

floor [ sqrt 3 ] + floor [ sqrt (4*3) ] =  1 + 3  = 4

 

If n = 4

floor [ sqrt 4] + floor [sqrt ( 4 *4) ] =  2 + 4  = 6

 

 

cool cool cool

 Sep 8, 2023
edited by CPhill  Sep 8, 2023

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