TY - JOUR
AU - Chowla, S. D.
AB - EEMARKS ON WARING'S THEOREM. 155 EEMAEKS ON WAEING'S THEOREM S. D. CHOWLA*. 1. Landau t has proved that every large N can be expressed in the form where all the c's are positive integers. I show here that by slight refine- ments of Landau's arguments we can prove Theorems I, II, III below. It seems that these theorems concerning, Waring's problem cannot be proved by the analytic method of Hardy and Littlewood. THEOREM I. To every large prime p there corresponds another primo p such that 216pip is a sum of six positive cubes. 3 2 THEOREM II . Every large N can be expressed in the form N= 2 cl, where every c is greater than THEOREM III. Every large N is a sum of eight positive cubes in at least gN* distinct ways, where g is a positive constant. Theorem II suggests the following interesting question. Is every large N expressible in the form 2(4, with all the c's greater than I * VN, 2+ where e is an arbitrarily small positive number ? It is plainly impossible for all the c's to be greater than • Received 4 November, 1929 ; read 16 November, 1929. t 
TI - Remarks on Warings Theorem
JF - Journal of the London Mathematical Society
DO - 10.1112/jlms/s1-5.2.155
DA - 1930-04-01
UR - https://www.deepdyve.com/lp/wiley/remarks-on-warings-theorem-N6IsO00ceu
SP - 155
EP - 158
VL - s1-5
IS - 2
DP - DeepDyve
ER -