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.)