The authors show that Bakirov's counterexample (which had been checked by211u001ecomputeralgebra methods up till order 53) to the conjecture that on nontrival 211u001esymmetry of an evolution equation implies infinitely many is indeed a 211u001ecounterexample. To prove this the authors use the symbolic method of Gel'fand-211u001eDikii and p-adic analysis. The authors also formulate a conjecture to the effect 211u001ethat almost all equations in the family considered by Bakirov have at most 211u001efinitely many symmetries. This conjecture depends on the solution of a 211u001ediophantine problem, which the authors explicitly state.
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