Question

The number of integers $a$ such that $1\le a\le 100$ and $a^a$ is a perfect square is

• A. $50$
• B. $53$
• C. $55$
• D. $56$

Answer 1

The correct option is C $55$

$1^1=1$ for $a$ as odd and $9^9,{25}^{25},{49}^{49},{81}^{81}$ are perfect square.

For $a$ as even integer.

We can hace all $a^a$ as perfect square.

So, all together $50+5=55$ such numbers.