Alice and Bob play the following game. They alternate selecting distinct nonzero digits (from 1 to 9) until they have chosen seven such digits, and then consider the resulting seven-digit number by concatenating the digits in the order selected, with the seventh digit appearing last (i.e. A1B2A3B4A6B6A7). Alice wins if and only if the resulting number is the last seven decimal digits of some perfect seventh power. Please determine which player has the winning strategy. modular arithmeticnumber theoryrelatively primenumber theory proposedprimitive root