anonymous
  • anonymous
Fool's problem of the day, If \( n \) and \( m \) are natural numbers such that \( 1 + 2 + 3 + … + n = m^2 \), Find the sum of digits of the greatest such \( n \) , smaller than \( 10^3 \).
Meta-math
chestercat
  • chestercat
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Mr.Math
  • Mr.Math
We're looking for a number \(m^2\) that's both triangular and perfect square. \(n<10^3 \implies m^2=\frac{n(n+1)}{2}<500500.\) The largest such \(m\) is \(41616\), that gives \(n(n+1)=2(41616) \implies n=288\). I cheated from here http://en.wikipedia.org/wiki/Square_triangular_number
anonymous
  • anonymous
That's interesting MR.Math, however the challenge was a develop a solution that could be implemented without electronic aid ;-)
Mr.Math
  • Mr.Math
I know, but I'm so lazy. Plus I know that a list of such numbers exist and there are not so many of them that are less than 500500. Steps to finding these numbers explicitly can be found in the link.

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anonymous
  • anonymous
lol, Mr.Math this is a quantitative aptitude problem, think elementary ;-)

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