The triangle problem

Number Theory Level 4

How many right angled triangles , with all sides an integer length in cm,have shortest side length 2007cm?

1 solution

Maria Kozlowska
Jan 21, 2016

$2007 = 3*3*223$

$a^2+b^2=c^2 \Rightarrow a^2=(c-b)(c+b) \Rightarrow (3*3*223)^2 = x(x+2*b)$

where $x = c-b$

There are 7 possible values for x: $1, 3, 9, 27, 81, 223, 669$

and possible values for $b$ are:

$2014024, 671340, 223776, 74580, 24824, 8920, 2676$

yes, this completes the set. nicely done.

SOURAV MISHRA - 5 years, 4 months ago