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).
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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)
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