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show that the diophantine equation $$2^a-3^b=5~~~~,a>5,b>3,a,b\in N^{+} $$ has no postive integers solution

maybe is old problem,But I try somedays,can't solve it by now

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Please see this paper of Herschfeld (pages 232 and 233) for a proof. The machinery used is elementary. I think the result was first proved by Pillai.

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