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Must x be an integer if 2^x and 3^x are integers?
Show that a real number x for which both 2^x and 3^x are integers must itself be an integer.
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| 1 | +{ | |
| 2 | + "domain": "mathematics", | |
| 3 | + "topics": [ | |
| 4 | + "number-theory" | |
| 5 | + ], | |
| 6 | + "type": "proof", | |
| 7 | + "cover": { | |
| 8 | + "motif": "blocks" | |
| 9 | + }, | |
| 10 | + "source": { | |
| 11 | + "key": "formal-conjectures", | |
| 12 | + "name": "Formal Conjectures", | |
| 13 | + "url": "https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/Mathoverflow/17560.lean", | |
| 14 | + "id": "Mathoverflow/17560", | |
| 15 | + "curator": "Google DeepMind and contributors", | |
| 16 | + "poser": "L. Alaoglu and P. Erdős (1944); asked on MathOverflow by Alon Amit", | |
| 17 | + "status": "open", | |
| 18 | + "as_of": "2026-10-20", | |
| 19 | + "catalog": "0521c19bbd38" | |
| 20 | + } | |
| 21 | +} | |