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> Solve the diophantine equation $3^x + 5^y = 7^z + 11^w$,here $x,y,z,w$ are all non-negative integers. 
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I find three solutions by force algorithm use Mathematica: (0,0,0,0)(1,1,1,0)(1,3,1,2).And there is no else when $y,z,w<100$.

Thanks in advance.