1Old question ...... no takers ?
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
21Any 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
11That'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.