Eulerian equality

We know that there are infinite Pythagorian triplets, that is numbers a, b, c such that

(1)   \begin{equation*} a^2 = b^2 +c^2 \end{equation*}

Let us investigate if there exist triplets such that

(2)   \begin{equation*} \varphi \left( a^2 \right) = \varphi \left( b^2 \right) + \varphi \left( c^2 \right) \end{equation*}

where \varphi denotes the Euler’s totient function.

Solution

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