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# Counting Divisible Subsets

Let $$a, b$$ be positive integers such that $$1 \leq b < a$$.

1. Let $$p$$ be an odd prime number. Find the number of subsets of $$\{1, 2, 3, \dots, ap\}$$ with $$bp$$ elements such that the sum of the elements of each subset is divisible by $$p$$.

2. Let $$n$$ be a positive integer. Find the number of subsets of $$\{1, 2, 3, \dots, an\}$$ with $$bn$$ elements such that the sum of the elements of each subset is divisible by $$n$$.

Note by Steven Yuan
1 year, 6 months ago