Since a>b,
a>(3/4)b
Multiply with b on both sides: ab>(3/4)b^2
  ab+(1/4)b^2>b^2
Add a^2 on both sides: a^2+ab+(1/4)b^2>a^2+b^2
  (a+0.5b)^2>M^2
for 'a', 'b' integers, M<(a+0.5b)

Figure 2: A proof of the theorem in Figure 1(b).