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GAPS BETWEEN DIVISIBLE TERMS IN $a^{2}(a^{2}+1)$
Published online by Cambridge University Press: 13 September 2019
Abstract
Suppose $a^{2}(a^{2}+1)$ divides $b^{2}(b^{2}+1)$ with $b>a$. We improve a previous result and prove a gap principle, without any additional assumptions, namely $b\gg a(\log a)^{1/8}/(\log \log a)^{12}$. We also obtain $b\gg _{\unicode[STIX]{x1D716}}a^{15/14-\unicode[STIX]{x1D716}}$ under the abc conjecture.
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- Research Article
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- © 2019 Australian Mathematical Publishing Association Inc.
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