It is observed that Φ(1)=1 and, Φ(2)=1, where Φ(x) denotes

**Euler's totient function**.

So for x=1, it is trivially observed that each of Φ(x) and Φ(x+1) is a perfect square.

(A) What is the next positive integer value of x such that each of Φ(x) and Φ(x+1) is a perfect square?

(B) What is the value of x with 2000 ≤ x ≤ 2100 such that each of Φ(x) and Φ(x+1) is a perfect square?

Given this tic-tac-toe position, as played by two expert players, who went first and where? Also, which was the last "move"?

X | O | O
---+---+---
| | X
---+---+---
| X | O

(An expert player is a player who would never play in such a way that would allow his opponent to win, and who would also try to get the possible best result.)