Any primitive solution (x,y,z) in positive integers to the equation x2+y2 = z2 is given by x = m2-n2, y = 2mn,z = m2+n2,where m and n are relatively prime positive integers such that m>n and m+n is odd.Again if (x,y,z) is a solution (kx,ky,kz) is also a solution. where k is a positive integer. I think this funda will be sufficient. i will try to solve later
Since I am posting after a long time , I am starting with a very elemental problem which is in fact incorrectly solved in Arihant ............... But I loved solving it ...........
Find the number of 2 numbers " x " and " y " out of the first 189 natural numbers that are two sides
of a right angled triangle .
Arihant has simply counted all of them !!!!!!!!!!!!!!!!!!!
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3 Answers
Shubhodip
·2011-06-17 05:12:05
Devil
·2011-07-20 21:51:36
That's not correct Subhodeep.
No where in the problem it's given that all the sides of the triangle are integers. Although I've no idea whether they meant it or not.