Find all the pairs ...

Algebra Level 3

Find all pairs ( m , n ) (m,n) of positive integers such that 2 m + 3 n { 2 }^{ m }+{ 3 }^{ n } is a square. The sum of all values of ( m , n ) (m,n) is

9 7 6 10

Shreya R by Shreya R , 21, India

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1 solution

Shubham Dwivedi
Oct 22, 2014

by observation we can say that the only possible solution is 16+9=25 thus m=4 and n=2

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I don't think that's a proper solution. Hint: check divisibility by 4 to prove that 'n' is even and then by 3 to prove that 'm' is even. The only possible solution is m=4 and n=2

Rayyan Shahid - 6 years, 7 months ago

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