You are given three integers A, B, C, Let's call a triple of integers (a,b, c) interesting if it satisfies the following criteria:
1) $1 \leq a \leq A, 1 \leq b \leq B, 1 \leq c \leq C$
2) for any two real numbers x and y such that x != 0 and y != 0,
$ax^2 + 2bxy + cy^2 > x^2 + y^2$ holds.
Problem: find number of triples $(a,b,c)$
I tried this problem but was unable to get the desired answer. Can anyone please help me in solving this?