# A Source Book in Mathematics, 1200-1800 by D. J. Struik

By D. J. Struik

These chosen mathematical writings conceal the years whilst the principles have been laid for the speculation of numbers, analytic geometry, and the calculus.

Originally released in 1986.

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**Extra resources for A Source Book in Mathematics, 1200-1800**

**Sample text**

And in general, if it is known that A < (p — 1)/», then one proves in the same way that we cannot have λ > (ρ — 1 )/(n + 1), therefore we must have λ = (ρ — 1)/(w + 1) or λ < (ρ — 1)(n + 1). 47. Corollary 3. Wherefrom it appears that the number of all numbers that cannot be residues is either = 0, or = λ, or = 2A or any multiple of A; for if there are more than ηλ of such numbers, then, if any at all, A new ones are added to them, so as to make their number = (η + 1)A; and if this does not yet comprise all the nonresidues, then at once A new ones are added.

I. We may consider the numbers χ and y as prime to each other; for if they had a common divisor, the cubes would also be divisible by the cube of that divisor. For example, let χ = 2α, and y = 26, we shall then have x 3 + y 3 = 8a3 + 863; now if this formula be a cube, a3 + 63 is a cube also. II. Since, therefore, χ and y have no common factor, these two numbers are either both odd, or the one is even and the other odd. In the first case, ζ would be even, and in the other that number would be odd.

On the enormous literature in this field see P. Bachman, Das Fermatproblem (De Gruyter, Berlin-Leipzig, 1919); L. J. Mordell, Three lectures on Fermat's last theorem (Cambridge University Press, Cambridge, England, 1921); It. Nogues, Theoreme de Fermat. Son histoire (Vuibert, Paris, 1932); H. S. Vandiver, "Fermat's last theorem," American Mathematical Monthly S3 (1946), 555-578. 9) how Euler proved Fermat's theorem for η = 3 and η = 4. Fermat communicated many of his results to the mathematician Bernard Frenicle de Bessy (1605-1675).