BMAD 65 Posted October 5, 2017 Report Share Posted October 5, 2017 For 0<x<y find an integer solution for x^y = y^x Quote Link to post Share on other sites

0 Solution Molly Mae 103 Posted October 6, 2017 Solution Report Share Posted October 6, 2017 12 hours ago, BMAD said: For 0<x<y find an integer solution for x^y = y^x Pretty easy answer: x=2, y=4 Quote Link to post Share on other sites

0 BMAD 65 Posted October 9, 2017 Author Report Share Posted October 9, 2017 (edited) On 10/5/2017 at 10:56 PM, Molly Mae said: Hide contents Pretty easy answer: x=2, y=4 is there another? Edited October 9, 2017 by BMAD Quote Link to post Share on other sites

0 Molly Mae 103 Posted October 9, 2017 Report Share Posted October 9, 2017 (edited) 3 hours ago, BMAD said: is there another? Not integers for 0>x>y Edited October 9, 2017 by Molly Mae Quote Link to post Share on other sites

0 Buddyboy3000 4 Posted October 9, 2017 Report Share Posted October 9, 2017 Spoiler Technically, there are an infinite amount of solutions for this equation. To find a solution, you can plug any value for the integer "a" to get a value for x and y. If "a" is any integer greater than 1, then the the solution is: x=^{a-1}sqrt(a) y=^{a-1}sqrt(a^a) Examples: a=1.5 x=2.25 y=3.375 2.25^3.375 = 3.375^2.25 = 15.43888... a=2 x=2 y=4 2^4 = 4^2 = 16 a=3 x=sqrt(3) y=sqrt(27) sqrt(3)^sqrt(27) = sqrt(27)^sqrt(3) = 17.36190... a=4 x=^{3}sqrt(4) y=^{3}sqrt(256) ^{3}sqrt(4)^^{3}sqrt(256) = ^{3}sqrt(256)^^{3}sqrt(4) = 18.80532... Quote Link to post Share on other sites

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## BMAD 65

For 0<x<y find an integer solution for

x^y = y^x

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