“School of Mathematics”
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| Paper IPM / M / 15826 |
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| Abstract: | |
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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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