Let $\varphi(x)$ be the Euler totient function and $a,b$ and $c$ be natural numbers.

**Question 1**: Are there infinitely many non-trivial solutions of

$$
\varphi(a)^2 = \varphi(b)^2 + \varphi(c)^2
$$

$$ \varphi(a^2) = \varphi(b^2) + \varphi(c^2) $$ A trivial solution is one which is obtained multiplying a smaller solution with a constant natural number.

The first few solutions are

```
(1004, 802, 604)
(1012, 782, 644)
(1050, 840, 630)
(1056, 816, 672)
(1084, 866, 652)
(1100, 850, 700)
(1136, 904, 688)
(1144, 884, 728)
(1188, 918, 756)
(1200, 960, 720)
```

**Question 2**: Is there a triplet with at least one of the three numbers $a,b$ and $c$ odd?

**Related question**: Pythagorean triples that “survive” Euler's totient function