Current Events > Here's a weird prime number calculus problem.

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FLOUR
04/27/23 6:10:47 PM
#1:


Suppose p and q are prime numbers such that p < q . Prove that there is a unique solution pair satisfying p^q < q^p .

And yes, calculus is involved or at least helps dramatically.

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Tyranthraxus
04/27/23 6:13:44 PM
#2:


p = 2 < q = 3

2^3 = 8 < 3^2 = 9

Why do I need calculus for this?

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KainWind
04/27/23 6:14:52 PM
#3:


I can't think of an example where that isn't true

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Momentai
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VampireCoyote
04/27/23 6:16:40 PM
#4:


those are actually letters

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She/her
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lderivedx
04/27/23 6:40:14 PM
#5:


It's because ln(x)-1 is negative when x < e.

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