For all positive integers $a,b$, given $a^b - b^a = 3$ Find all possible values of $a$ and $b$
I tried to simulate this using a program and found the one fit $a = 4$ and $b = 1$. Would love to see a Mathematical solution for it. Please help.
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According to Wolfram Alpha, the only integer solutions are $a=4, b=1$ and $a=1, b=-2$. Not sure how to go about proving that though – wjmccann Jun 29 '18 at 06:01
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Positive integers so a=4 and b=1 seems to be the only fit – vivekv Jun 29 '18 at 06:07
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My mistake not sure how I glossed over that positive integers – wjmccann Jun 29 '18 at 06:09
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3Possible duplicate of Find integral solution of $a^{b} - b^{a} = 3$ and Find all solutions in positive integers to $a^b -b^a = 3$ – Sil Jun 29 '18 at 06:16