Online Course Discussion Forum

MCIII Number Theory 3.18

 
 
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MCIII Number Theory 3.18
by Tina Jin - Friday, 5 January 2024, 3:30 PM
 

Hello,

This is what I did for this problem:

Why does only k=0, 1, 2 work, but why?

Thanks,

Tina Jin

 
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Re: MCIII Number Theory 3.18
by Dr. Kevin Wang - Saturday, 6 January 2024, 12:05 AM
 

For each $m$ as the value of $\lfloor\sqrt{n}\rfloor$, $k=0,1,2$ represent the numbers $m^2$, $m^2+m$, and $m^2+2m$.  The next value, $m^2+3m$, is already greater than $(m+1)^2$, and if $n=m^2+3m$, $\lfloor\sqrt{n}\rfloor$ is greater than $m$, so it is no longer a solution for $\lfloor\sqrt{n}\rfloor = m$.

Picture of Tina Jin
Re: MCIII Number Theory 3.18
by Tina Jin - Sunday, 14 January 2024, 10:30 AM
 

Oh! I get it, thank you!