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MR1257577 11D41 (11B68 11Y50)
Moree, P.; te Riele, H. J. J.; Urbanowicz, J. Divisibility properties of integers $x,\ k$ satisfying $1^k+\cdots+(x-1)^k=x^k$. Math. Comp. 63 (1994), no. 208, 799–815.
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