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math.NT2010★ 2 cited
Products of shifted primes simultaneously taking perfect power values
Tristan Freiberg
Let be an integer and let be a finite, nonempty set of nonzero integers. We will obtain a lower bound for the number of squarefree integers , up to , for which…
math.NT2010★ 2 cited
Strings of congruent primes in short intervals
Tristan Freiberg
Fix ε> 0, and let p_1 = 2, p_2 = 3,... be the sequence of all primes. We prove that if (q,a) = 1 then there are infinitely many pairs p_r, p_{r+1} such that p_r \equiv p_{r+1} \equ…