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| Title: | Mathematics at DEC |
|
| Moderator: | RUSURE::EDP |
|
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
347.0. "Ramanujan pairs" by TOOLS::STAN () Thu Oct 17 1985 14:18
(John Brillhart)
Let {a[i]}, i=1..m and {b[j]}, j=1..n be increasing sequences of
positive integers. It is known that
m a[i] n b[j] j
PROD 1/(1-x ) = 1 + SUM x /(1-x)...(1-x )
i=1 j=1
exactly if m=n and a[i]=b[i]=i for i=1..n. In other words, the
only possibility is the Euler identity.
Is this true if you take (the coefficients on) the two sides of
the equation modulo 2? I.e. are there other identities mode 2? mod 3?
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