MathLabs

Problem 5

Find all pairs (a,b)(a,b) of positive integers satisfying ab2=ba a^{b^2}=b^a .
Step 5 of 5: Check the answers
Previous stepNext step
In plain words

Check the answers

(1,1),(16,2),(27,3)(1,1),(16,2),(27,3)
Detailed analysis

Direct substitution verifies 11=11^{1}=1, 1622=21616^{2^2}=2^{16}, and 2732=32727^{3^2}=3^{27}. These are all solutions.