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(338) 6

Part of 1992 Tournament Of Towns

Problems(1)

TOT 338 1992 Spring A S6 no of decompositions in product of integers

Source:

6/9/2024
For natural numbers nn and bb, let V(n,b)V(n, b) denote the number of decompositions of nn into the product of integers each of which is greater than bb: for example 36=6×6=4×9=3×3×4=3×12,36 = 6\times 6 = 4\times 9 = 3\times 3\times 4 = 3\times 12, i.e. V(36,2)=5V(36,2) = 5. Prove that V(n,b)<n/bV(n, b) < n/b for all nn and bb.
(N.B. Vasiliev, Moscow)
number theorycombinatorics