(\(1\)) If \(a,b\) and \(c\) are real numbers such that \(a<b<c\), \(a+b+c=6\) and \(ab+bc+ca=9\).

Prove that \(0<a<1<b<3<c<4\).

(\(2\)) Find all triples (\(a,b,c\)) such that

\[\left(1+\frac{1}{a}\right)\left(1+\frac{1}{b}\right)\left(1+\frac{1}{c}\right)=2\]

(\(3\)) How many perfect squares are there \(\pmod{ 2^n}\)?

Please post your solutions!

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