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RU-ALLRUSSIAN 1988 Problem 6

  • Answer

The numbers 1 and 2 are written on an empty blackboard. Whenever the numbers m and n appear on the blackboard the number m+n+mn\mathrm{m} + \mathrm{n} + \mathrm{mn} may be written. Can we obtain (1) 13121, (2) 12131?

Dataset text NuminaMath olympiads. Quoted with source.

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13121 = 2^{a}3^{b} - 1, 12131 \neq 2^{a}3^{b} - 1

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