%0 Journal Article
%T 关于不定方程5<i>x</i>(<i>x</i><i> </i>  1)(<i>x</i><i> </i>  2)(<i>x</i><i> </i>  3) = 42<i>y</i>(<i>y</i><i> </i>  1)(<i>y</i><i> </i>  2)(<i>y</i><i> </i>  3)<br>On the Diophantine Equation 5<i>x</i>(<i>x</i><i> </i>  1)(<i>x</i><i> </i>  2)(<i>x</i><i> </i>  3) = 42y(<i>y</i><i> </i>  1)(<i>y</i><i> </i>  2)(<i>y</i>   3)
%A 张艺宝
%J Advances in Applied Mathematics
%P 2105-2109
%@ 2324-8009
%D 2024
%I Hans Publishing
%R 10.12677/aam.2024.135198
%X 本文运用同余式、递推序列和Pell方程等初等方法，证明了不定方程5<i>x</i>(<i>x</i><i> </i> 1)(<i>x</i><i> </i> 2)(<i>x</i><i> </i> 3) = 42<i>y</i>(<i>y</i><i> </i> 1)(<i>y</i><i> </i> 2)(<i>y</i> 3)仅有唯一正整数解(<i>x</i>, <i>y</i>) = (6, 3)，并找出了该方程的所有整数解。<br />
This article uses elementary methods such as congruence formula, recursive sequences, and Pell equation to prove that indefinite Diophantine equation 5<i>x</i>(<i>x </i> 1)(<i>x </i> 2)(<i>x </i> 3) = 42<i>x</i>(<i>x </i> 1)(<i>x </i> 2)(<i>x </i> 3) has a unique positive integer (<i>x</i>, <i>y</i>) = (6, 3). Also, All 20 groups of integer solutions of the equation are found.
%K 不定方程，同余式，Pell方程，正整数解<br>Diophantine Equation
%K Congruence Formula
%K Pell Equation
%K Positive Integer Solution
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=87681