MathLabs

Problem 5

Find all pairs (a,b)(a,b) of positive integers satisfying ab2=ba a^{b^2}=b^a .
Step 1 of 5: Handle the unit case
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In plain words

Handle the unit case

(a,b)=(1,1)(a,b)=(1,1)
Detailed analysis

If a=1 a=1 or b=1 b=1, the equation forces the other number to be 11. Hence (1,1)(1,1) is a solution; assume a,b>1 a,b>1 below.