Abstract
TextIn this paper, the following results are proved: (i) For any odd integer ℓ with at most two distinct prime factors and any positive integer n, the product (1ℓ+1)(2ℓ+1)⋯(nℓ+1) is not a powerful number; (ii) For any integer r≥1, there exists a positive integer Tr such that, if ℓ is a positive odd integer with at most r distinct prime factors and n is an integer with n≥Tr, then (1ℓ+1)(2ℓ+1)⋯(nℓ+1) is not a powerful number. VideoFor a video summary of this paper, please visit http://youtu.be/nU-nkxNX1BA.
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