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\(\text{Find the number of positive integers $n \le 1000$ such that $15n$ is a perfect square.}\)

 Sep 17, 2019

Best Answer 

 #1
avatar+6046 
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\(\text{$15=3\cdot 5$ so $15n$ being a perfect square means $n=15 k^2$}\\ \text{We want all of these up to 1000}\\ 15k^2 \leq 1000\\ k^2 \leq 66\frac 2 3\\ k\leq 8\\ \text{So we have $n = 15,60, 135, 240,375,540,735,960$}\)

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 Sep 17, 2019
 #1
avatar+6046 
+1
Best Answer

\(\text{$15=3\cdot 5$ so $15n$ being a perfect square means $n=15 k^2$}\\ \text{We want all of these up to 1000}\\ 15k^2 \leq 1000\\ k^2 \leq 66\frac 2 3\\ k\leq 8\\ \text{So we have $n = 15,60, 135, 240,375,540,735,960$}\)

Rom Sep 17, 2019

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