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LollyLau
 4 years ago
Series of trialanderror questions:
Find all the unknowns for:
1. x^y=y^x
2. x^y=y^x+1
where all the unknowns are integers.
LollyLau
 4 years ago
Series of trialanderror questions: Find all the unknowns for: 1. x^y=y^x 2. x^y=y^x+1 where all the unknowns are integers.

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i guess \[y=x\] might work for first one

LollyLau
 4 years ago
Best ResponseYou've already chosen the best response.0let's say they aren't, some actual answers please...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0what is wrong with \[3^3=3^3\]?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.02 and 4 works for the first one.

LollyLau
 4 years ago
Best ResponseYou've already chosen the best response.0Nothing! Pratu got it right :) (Well you too...)

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.2Sorry, I thought it was a system of two equations.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ooooooooooooooh. i was wondering...

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.2I agree with satellite on the first one, the solution of the first one is all integers (x,y) such that x=y. For the second one, we have (x,y)=(2,1) is a solution.

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.2(3,2) is another solution.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0pratu had \[2^4=4^2\] so that works as well. my guess is there are no others, but that is a guess

LollyLau
 4 years ago
Best ResponseYou've already chosen the best response.0no proof tho. just know that for SURE :)

LollyLau
 4 years ago
Best ResponseYou've already chosen the best response.0Mr. Math, you're missing one more answer. (which i know)

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.2Actually any solution in the form (x,0), x is a positive integer.

LollyLau
 4 years ago
Best ResponseYou've already chosen the best response.0Can we do this for +2, +3, +4 etc.
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