a) Prove that for all n E N, the number n' + 5n is divisible by 6. b) Prove that n K n +2 2 =2- k= 1 c) The following picture shows ruble bills from the former Soviet Union. # 8739178 Allarb Pyb/EH Prove that every full-ruble amount of at least 8 rubles can be paid using only 3-ruble and 5-ruble bills