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$2^1+3^1=5^1$

$2^4+3^2=5^2$

In these cases a power of $2$ plus a power of $3$ is a power of $5$. If I understand the abc conjecture correctly, this is only finitely often the case.

Question 1: Is there an easy proof for this?

Question 2: Are there other known solutions of $2^k+3^m=5^n$?

Hunz
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    Similar: http://math.stackexchange.com/questions/662121 (case $k$ even), http://math.stackexchange.com/questions/348538, http://math.stackexchange.com/questions/350987 – Bart Michels Oct 28 '16 at 22:52
  • A couple of times there were a proof for this in general mentioned. Maybe you try to find that references using the tag diophantine... – Gottfried Helms Oct 29 '16 at 10:44

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