For non-equal, natural numbers. Here’s a plot of numbers for which this works:pic.twitter.com/oK7JY49l2R
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For non-equal, natural numbers. Here’s a plot of numbers for which this works:pic.twitter.com/oK7JY49l2R
Unrelated fun fact: In 1769 Euler conjectured that A⁴+B⁴+C⁴=D⁴ has no solution in natural numbers. In 1986, Noam Elkies found the smallest counterexample: 2682440⁴ + 15365639⁴ + 18796760⁴ = 20615673⁴
And in 1988, Roger Frye found the smallest possible counterexample 95800⁴ + 217519⁴ + 414560⁴ = 422481⁴
Where a ≠ b.
Fun fact: if a=(1+1/n)^n and b=(1+1/n)^(n+1), then a^b=b^a. In fact, if you let n vary over the integers, this gives all the rational solutions (where a≠b).
If you graph x^y=y^x, you'll notice that x=y branch intersects the other one at (e,e). My last tweet is why.pic.twitter.com/icUjkaGfc9
Only if numbers are natural and not equal. For example 2^-0.7666 = - 0.7666^2 (0.7666 is a real number that continues)
How did U find this ??
sqrt(27)^sqrt(3) = sqrt(3)^sqrt(27)
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