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Diophantine Equation (Posted on 2013-05-14) Difficulty: 2 of 5
Solve in Integers

(5+3√2)m = (3+5√2)n

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution This should work Comment 1 of 1
The only solution is (m,n)=(0,0)

A^m = B^n
m*log(A) = n*log(B)
m/n = log(B)/log(A)

But log(5+3√2)/log(3+5√2) is clearly irrational so there are no integers m/n with n≠0.

A good approximation is 10117/9741 as supplied by

  Posted by Jer on 2013-05-14 12:45:34
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