3

Part of 2011 Puerto Rico Team Selection Test

Problems(2)

Puerto Rico 2011 TST Problem 3

Source:

(a) Prove that (p^2)-1 is divisible by 24 if p is a prime number greater than 3. (b) Prove that (p^2)-(q^2) is divisible by 24 if p and q are prime numbers greater than 3.

number theoryprime numbersalgebra unsolvedalgebra

Puerto Rico IBERO TST Problem 3

Source:

1234

is written on the board. A play consists of subtracting a non-zero digit of that number from that number, and replacing the number by the result. The player who writes the number (not digit) zero wins. Determine if there is a winning strategy for one of the two players who play consecutively.
Please remember to hide your solution. (by using the hide tags of course.. I don't literally mean that you should hide it :ninja: )