# solutions to n +a(1) +a(2) +..+a(j) = a(1)a(2)..a(j)
Leroy Quet
qq-quet at mindspring.com
Tue Sep 23 03:59:44 CEST 2003
Let n and j be any fixed positive integers.
How many sequences of j positive integers
{a(1), a(2), ...,a(j)}
satisfy the equation:
n +a(1) +a(2) +a(3) +..+a(j) =
a(1) *a(2) *a(3) *...*a(j)
?
Fixing j and finding a closed-form of the number of solutions in-terms of
n might be interesting.
For example, for j = 2, the number of solutions is
d(n+1), the number of positive divisors of (n+1).
(I think.)
There must be a recursive-definition, anyhow, to find the number of
solutions with j a's (in terms of n) from the numbers of solutions for
(j-1) a's, as a possibility.
Thanks,
Leroy Quet
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