A binomial number is a number of the form a^n ± b^n, where a, b, and n are integers. Binomial numbers can be factored algebraically as a^n - b^n = (a - b)(a^(n - 1) + a^(n - 2) b + ... + a b^(n - 2) + b^(n - 1)) for all n, a^n + b^n = (a + b)(a^(n - 1) - a^(n - 2) b + ... - a b^(n - 2) + b^(n - 1)) for n odd, and a^(n m) - b^(n m) = (a^m - b^m)[a^(m(n - 1)) + a^(m(n - 2)) b^m + ... + b^(m(n - 1))]. for all positive integers m, n.
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