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Mathematics 12 Online
OpenStudy (anonymous):

Why is this true: The kth differences of the sequence 1^k, 2^k, 3^k,... are all equal to k! taken from here: http://en.wikipedia.org/wiki/Proofs_of_Fermat%27s_theorem_on_sums_of_two_squares near the end of Euler's proof. Am I to take it that (k+1)^k-k^k = k! ?

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