Difference between revisions of "2023 IOQM/Problem 4"

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(Solution1(Diophantine))
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Find the maximum possible value of <math>x + y</math>.
 
Find the maximum possible value of <math>x + y</math>.
 
==Solution1(Diophantine)==
 
==Solution1(Diophantine)==
<cmath>x^{4}=(x-1)(y^{3}-23)-1</cmath>
+
<math>x^{4}=(x-1)(y^{3}-23)-1</math>

Revision as of 12:48, 19 October 2023

Problem

Let $x, y$ be positive integers such that \[x^{4}=(x-1)(y^{3}-23)-1\]

Find the maximum possible value of $x + y$.

Solution1(Diophantine)

$x^{4}=(x-1)(y^{3}-23)-1$