Problem 3 (1010101 is always composite!). The goal of this problem is to show that for any bases b > 2, the number 1010101 is composite. We see this is true base 10, 2, and 3 since 101010110 = 1.106 +1.104 +1.102 +1. 10 = 1010101 = 73 - 101. 137 10101012 = 1.26 +1-24 +1 -22 +1 -2 = 85 = 5 - 7 10101013 = 1 : 36 +1.34 +1.32 +1 -30 = 820 = 22.5.7 a. Show that in base b = 4,5,6,7, we have 1010101, is composite. (You may use SAGE To factor the resulting number) b. Show that in any basis the number 10101016 cannot be prime. (Hint: How does 66 +64 +62 +1 factor?) c. (Bonus) How about the number 11010101? For 2