Journal of the Australian Mathematical Society (Series A)

Research Article

Some problems in partitio numerorum

P. Erdösa1 and J. H. Loxtona2

a1 Mathematical Institute Hungarian Academy of Science Budapest Humgary

a2 School of Mathematics University of New South Wales Kensington, N.S.W., Australia


We consider some unconventional partition problems in which the parts of the partition are restricted by divisibility conditions, for example, partitions n = a1+…+ak into positive integers a1, …, ak such that a1 ∣ a2 ∣ … ∣ ak. Some rather weak estimates for the various partition functions are obtained.

(Received April 24 1977)

Subject classification (Amer. Math. Soc. (MOS) 1970)

  • 10 A 45;
  • 10 J 20