As you may have guessed, there is a point where Fahrenheit and Celsius coincide: -40°C = -40°F. Mathematically, this can be shown thus: since C = (5/9) * (F - 32), and since F = -40, then:
C = (5/9) * (-40 - 32)
C = (5/9) * (-72)
C = -360/9
C = -40

Since Celsius and Fahrenheit converge at one point, surely Fahrenheit and Kelvin do too? Well, yes. Since K=C + 273.15 (and hence C=K - 273.15), then:
K - 273.15 = (5/9) * (F - 32)
K = F ∴ K - 273.15 = (5/9) * (K - 32)
K = (5K/9) - (32*5)/9 + 273.15
4K/9 = 273.15 - 160/9
4K = 9(273.15) - 160
K = 2458.35/4 - 40
K = 614.5875 - 40
K = 574.5875
Hence, 574.5875K = 574.5875°F

Thanks to rootbeer277 for pointing out my error to me, and to Wntrmute, krimson, AspieDad and jrn for letting me know where I went wrong.

PS: 1Amidala24601Fan has sent me this little bit of trivia regarding the Celsius and Rankine scales (where Rankine is to Fahrenheit as Kelvin is to Celsius, i.e. 0°Ra = 0K = absolute zero):
C = (Ra - 491.67) * (5/9) (the proof, given only what I've already written about, is trivial but messy and will not be shown here)
C = Ra ∴ C = (C - 491.67) * (5/9)
C = (5C/9) - (2458.35)/9
4C/9 = -(2458.35/9)
4C = -2458.35
C = -614.5875

This is, of course, impossible.