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Possible $\mathsf{NP}$ complete problem from number theory

A candidate $\mathsf{NP}$ complete variant of factoring was posted in https://cstheory.stackexchange.com/questions/4769/an-np-complete-variant-of-factoring, where decision problem $\text{BOUNDED-...
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Is this factorization problem in EXP?

Factorization is not known to have a polynomial time algorithm. Traditionally the input length is number of bits in representation of the integer to be factored. However now consider integers of form $...
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