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For a certain positive integer \(m,\) the equation \(\lfloor \sqrt{n} \rfloor = m\) has 137 solutions in integers \(n.\) Find \(m.\)

 May 9, 2019
 #1
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n=4624; c=0; a=floor(sqrt(4624));printc," - ",  n," ", a;c=c+1;n++;if(n<4761, goto2, discard=0;

Floor(137 / 2) =68 
m = 68.
69^2 - 68^2 =137
4,761 - 137 =4,624, so:
n=4,624

 May 9, 2019
 #2
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The floor of 137/2 is 68.

So m=68.

 

You are very welcome!

:P

 May 9, 2019

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