I'm having difficult with the following question :

A. Show that the number of partitions of n where in each one of them the even numbers appears at most once equals to the number of partitions of n in which every number appears at most three times .

B. show that the number of partitions of n to sizes of 3,5,7,9,... equals to the number of partitions of n to partitions of size that are not equal to 1,2,4,8,...