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Number Theory 184 (2018), 473–484

Tsz Ho Chan, Stephen Choi, Peter Cho-Ho Lam, Divisibility on th e sequence of perfect squares minus one: The gap principle, J · 2018

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Gaps between divisible terms in $a^2 (a^2 + 1)$

math.NT · 2019-06-26 · unverdicted · novelty 5.0

Proves b ≫ a (log a)^{1/8} / (log log a)^{12} whenever a²(a²+1) divides b²(b²+1) with b>a, plus a power-saving bound under the abc conjecture.

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  • Gaps between divisible terms in $a^2 (a^2 + 1)$ math.NT · 2019-06-26 · unverdicted · none · ref 2

    Proves b ≫ a (log a)^{1/8} / (log log a)^{12} whenever a²(a²+1) divides b²(b²+1) with b>a, plus a power-saving bound under the abc conjecture.