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In this paper, we demonstrate that 1 is the only integer that is both triangular and a repunit.
We are interested whether there is a nonnegative integer and an infinite sequence of digits in base such that the numbers where are all prime or at least do not have prime divisors in a finite set of prime numbers If any such sequence contains infinitely many elements divisible by at least one prime number then we call the set unavoidable with respect to . It was proved earlier that unavoidable sets in base exist if and that no unavoidable set exists in base Now, we prove...
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