History Of The Theory Of Numbers - I

CHAP, xvi] FACTORS OP an*b\ 387
A. Cunningham66 factored 5n— 1 for w = 75, 105.
L. Kronecker560 proved that every divisor, prime to t, of (1) is s 1 (mod t) . H. S. Vandiver666 noted that the proof applies to the homogeneous form Ft(a, 6) of (1) if a, b are relatively prime.
D. Bidolle87 gave a defective proof that 3-24l+l is a prime.
The Math. Quest. Educational Times contains the factorizations of:
Vol. 66 (1897), p. 97, 2185-1 factor 312. Vol. 68 (1898), p. 27, p. 112, 2720-!; p. 114, W**+4.
Vol. 69 (1898), p. 61, 382M-1; p. 73, rf-1, z=500, 2000; p. 117, x*+y*; p. 118, 1018+33, 33.1018+1.
Vol. 70 (1899), p. 32, p. 69, 242*+ 1; p. 47, 32015-1; p. 64, 222+l, 8l4+l, 20018+1; p. 72, 2014-1; p. 107, 97216+1. Vol. 71 (1899), p. 63, a4"*2-!; p. 72,
Vol. 72 (1900), p. 61, (3n)4w-l factor 24n+l if prime; p. 86, 72210+1; p. 117, 144010+1.
Vol. 73 (1900), p. 51, 3520+1; p. 96, 7U-1; p. 104, p. 114, x*+tf.
Vol. 74 (1901), p. 27, a prime 2«g+l divides g*~l if fc=2«-1; p. 86, x10~5V°.
Vol. 75 (1901), p. 37, oH-y4; p. 90, 17927+1; p. Ill, 786+l. [Educ. Times, (2), 54, 1901, 223, 260].
Ser. 2, Vol. 1 (1902), p. 46, 10082'+!; p. 84, tf+ny*. Vol. 2 (1902), p. 33, p. 53, #*+!; p. 118, 1188+1.
Vol. 3 (1903), p. 49, a4+64 (cl. 74, 1901, 44); p. 114, a8+l, a=60000.
Vol. 6 (1904), p. 62, 9618+1.
Vol. 7 (1905), p. 62, 20818-1; pp. 106-7, 2™+l.
Vol. 8 (1905), p. 50, 9618+1; p. 64, 212«+1.
Vol. 10 (1906), p. 36, 5418+1, 6W+1.
Vol. 12 (1907), p. 54, 642+l, 2480+1.
Vol. 13 (1908), p. 63, 106-7, 364+264.
Vol. 14 (1908), p. 17, 15018+1; p. 71, sextics; p. 96, 785+l.
Vol. 15 (1909), p. 57, 3M+2M; p. 33, 3m+l, 1245+1; p. 103, 2821+1, 44ll+l, 630+1.
Vol. 16 (1909), p. 21, 1924+1.
Vol. 18 (1910), pp. 53-5, 102-3, z4+42/4; pp. 69-71, z6+27yfl; p. 93, y16-!.
Vol. 19 (1911), p. 103, x3+2/3 = «8+«;8. Vol. 23 (1913), p. 92, (x*-Nx±N
Vol. 24 (1913), pp. 61-2, x™±y\ t/ = 5, 7, 11, 13; pp. 71-2, zl2+2«, x18+39,
Vol. 26 (1914), p. 23, x2Jfc+l for fc = 67i+3^3v; p. 39, s12+66; p. 42, rc10-56, x14+77, z22+llu, x26- 1313. Vol. 27 (1915), pp. 65-6, 4518-1, 2026- 1, fc30+l for k = 6, 8, 10; p. 83, o^+42/4 (when four factors). Vol. 28 (1915), p. 72, 5030+1. Vol. 29 (1916), p. 95, 9618+1.
New series, vol. 1 (1916), p. 86, z20+10l°, x28+1414; pp/94-5, x30-515, a^+lS15.
Vol. 2 (1916), p. 19, a^-S15.
Vol. 3 (1917), p. 16, a;16-?/16; p. 52, xll-l.
E. B. Escott58 gave many cases when 1+z2 is a product of two powers of primes or the double of such a product.
MProc. London Math. Soc., 34, 1901, 49.
^Vorlesungen iiber Zahlentheorie, 1, 1901, 440-1.
M&Amer. Math. Monthly, 10, 1903, 171.
"Messenger Math., 31, 1901-2, 116 (error); 33, 1903-4, 126.
"L'interme'diaire des math., 7, 1900, 170.