Chap. XVI] FACTORS OF a** ±6". 391 
A. Cunningham^Habulated factors of y^=^l,x'^=^y''", and gave an account 
of printed and manuscript tables of solutions of 2/"*='=l = (mod p^). 
Cunningham^^ tabulated factors of x^^^y"" for x^lQ and certain y's as 
high as 31 when x = 2 or 4, where x, y are relatively prime and x> 1, y> 1. 
Cunningham^^ noted that x-2''+l is composite for l<a;<233, x 9^ 14:1. 
A. Cunningham and H. J. WoodalP^ tabulated factors of 2'^^q and 
g.2*±l for 5-^66, and tabulated values of q for which one of these four 
functions is divisible by a given prime p or power of p. They confirmed 
that X.2'' + 1 is composite when 1< x< 233 except perhaps when x = 141 . In- 
cidentally (p. 15), the factors of 2*"^^; — 1 for A; ^ 17 are given. 
For factors of 2^ — 1 and 10" — 1, see Chapters I and VI. For factor 
tables of numbers m.2^±l, see Seelhoff^^ ^^^ Morehead^o of Ch. XIII; for 
m. 6^=1=1, Dines^^ For factors of several numbers d^ — 1, see Lawrence^^, 
Biddle^^ and Kraitchik^i of Ch. XIV. For the form of factors of a'^+b" 
when k = 2^, see Euler" of Ch. XV. Various results in Ch. XVII relate to 
factors of a'*=t5'». 
Factors of Trinomials. 
Seven^^ primes p such that (p^ — 1)^ has 4 or more factors px+l,x<p. 
List^^ of algebraically factorable trinomials x^+xy'^+y^, etc. 
Factors" of 14^14^+1, 7^+2-7'+l, etc. 
Conditions that x^-\-Px'^-\-c^ be a product of 4 rational quadratic factors.^^ 
Two^^ factors of x^-{-i4:m'^+Sm^+2)xY+y\ 
Factors^"*^ of various trinomial expressions. 
For factors of x'^+Qbx^+b^ see Dirichlet^ of Ch. XVII. See papers 28, 
28a, 65, 89 above. 
8«Messenger Math., 45, 1915, 49-75. 
^Ubid., 185-192. 
ssProc. London Math. Soc, (2), 4, 1907, xviii; (2), 15, 1916-7, xxix. 
s^Messenger Math., 47, 1917, 1-38. Math. Quest. Educ. Times, (2), 10, 1906, 44. 
»5Math. Quest. Educat. Times, (2), 15, 1909, 82-3. Amer. Math. Monthly, 15, 1908, 67, 138. 
L'intermediaire des math., 15, 1908, 121. 
9«Math. Quest. Educ. Times, (2), 16, 1909, 39-41. 
»Ubid., 65-6. 
«8/6id., (2), 18, 1910, 64-5; (2), 22, 1912, 20-1. 
s^Sphinx-Oedipe, 6, 1911, 8-9. 
""Math. Quest. Educ. Times, 72, 1900, 26-8; 74, 1901, 130-1; (2), 6, 1904, 97; 19, 1911, 85; 
20, 1911, 25-6, 76-8; 22, 1912, 54-61. Math. Quest, and Solutions, 3, 1917, 66; 4, 1917, 
13,39; 5, 1918, 38, 50-1. 
