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The formulas mentioned in Gauss's note are not the modular equation of order 7, but a very close one; the formula for $A$ is in fact the "Multiplier equation" .The point is that confirming that $P(B,b) = 0$ (not $P(A,b)$; the equation $P(B,b) = 0$ was not written by me in the posted question) is the modular equation of order 7 would be much easier, ...


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The article "Is lens design legal?" gives some details about Gauss's letter to Brandes; although it doesn't explain much about Gauss's formulas and calculations, it describes very well the historical significance and meaning of this letter. The article discusses "figures of merit" of optical systems; a kind of quantitive measure of the ...


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