SOLUTION: If m and k are integers, what are all the solutions to the equation {{{9(7^k+7^(k+2))= 5^(m+3)+5^m}}}

Question 1114882: If m and k are integers, what are all the solutions to the equation
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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If m and k are integers, what are all the solutions to the equation
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 =   ====>


 = 


 =   ====>   Divide both sides by 9  ====>


 =   ====>


 =   ====>  Comparing prime factors and their degrees and using the theorem on uniqueness 
                         of decomposition integers into the product of their prime factors


Answer.  m = 2,  k = 1.

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