求证:\(y＞\sqrt{\frac{\left( 2^a+1\right)^2+3}{\left( 2^m+1\right)^2+3}}\)

太阳

已知:偶数\(a＞0\)，\(c＞0\)，\(m＞0\)，\(t＞0\)，\(a＝c^2\)，\(a\ne m\)
方程\(\frac{\left( 2^a+1\right)^2+3}{\left( 2^m+1\right)^2+3}＝t\)，有唯一的正整数解，\(\sqrt{a}＝m\)
\(\frac{\left( 2^a+1\right)^2+3}{\left( 2^m+1\right)^2+3}\)的最大质因数是\(y\)
求证:\(y＞\sqrt{\frac{\left( 2^a+1\right)^2+3}{\left( 2^m+1\right)^2+3}}\)