Sunday, January 12, 2014

Q2014/003) How many positive integers are there , for: a^2=9555^2+c^2


9555=357^213
So 
9555^2=3^25^27^413^2
This has (2+1)(2+1)(4+1)(2+1) or 135 factors out of which one is 9555 and 67 are below 9555 and 67 are above 9555
(a + c) > 9555 and (a-c) < 9555 is a set of solution
So number of solutions 67
For a-c  we need to take
3x5y7z13m (x,y,z,m to be chosen based on limit for example x between 0 and 3 such that a +c > 9555) and for a-c it is 9555^2/(a+c)

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