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“School of Mathematics”

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Paper   IPM / M / 15826
School of Mathematics
  Title:   On the factorization of x2+D
  Author(s):  Amir Ghadermarzi
  Status:   Published
  Journal: Bull. Aust. Math. Soc.
  Vol.:  100
  Year:  2019
  Pages:   206-215
  Supported by:  IPM
  Abstract:
Let D be a positive nonsquare integer, p a prime number with p \nmid D, and 0 < σ < 0.847. We show that there exist effectively computable constants C1 and C2 such that if there is a solution to x2+D=pn with pn > C1, then for every x > C2 with x2+D=pn ·m , we have m > xσ. As an application, we show that for x ≠ {1015,5 }, if the equation x2+76=101n.m holds, we have m > x0.14.

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