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5 results on '"exponential equations"'

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1. Sums of two $S$-units via Frey-Hellegouarch curves

2. On a conjecture on exponential Diophantine equations

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3. Linear equations with unknowns from a multiplicative group whose solutions lie in a small number of subspaces

4. On equal values of power sums of arithmetic progressions

5. On the singularity of generalised Vandermonde matrices over finite fields