Being a number theorist, I have invested $1000 into cryptocurrency, widely known to be the best get-rich-quick method. Each week, the value of my investment multiplies by 5. Being a cautious fellow, whenever I have accumulated enough money in my investment account, I buy as many gold bars as I can (at $29,000 each) and bury them in my backyard. Will I ever have exactly $13,000 in my investment account? If so, when? Solve this problem by finding a primitive root and doing index arithmetic.