Re: 3435 = 3^3 + 4^4 + 3^3 + 5^5
- From: "Dave L. Renfro" <renfr1dl@xxxxxxxxx>
- Date: Wed, 9 Sep 2009 11:07:54 -0700 (PDT)
Jim Ferry wrote:
Yes, I thought there'd be more cases too. Turns out there
were only 184,755 (in my version -- there could be fewer still),
which took about 7 seconds to check on my laptop.
I saw this number curiosity in a late 1980s issue of
the journal "Mathematical Spectrum", but I didn't write
down the specific reference and I've since returned the
volume to the library. However, in a latter issue of the
same journal, which I presently have with me, I came
across a follow-up note, which I've given in full below.
The note appears in Volume 22, Number 2 (1989/90), p. 60.
*************************************************************
'Curiouser and curiouser', said Alice
Malcolm Smithers has previously sent us the curious number
3435 = 3^3 + 4^4 + 3^3 + 5^5.
He has since written to tell us that this is the only
number known of this type, apart from 1^1 = 1. Curiously,
the binary representation of 3435 is
110101 101011
53 43
*************************************************************
By the way, I hate sloppy language like this: "the only
number known of this type". Does this mean it's the only
number Smithers knows of, the only number Smithers and the
editor know of, or that Smithers (or someone else) has
managed to prove that it's the only number? My guess is
the last interpretation, but a mathematics journal editor
should know better than to write in such an ambiguous way.
So should a mathematics author, but most definitely a
mathematics editor. Even a non-mathematics editor, for
that matter, although perhaps not a non-mathematics author.
Dave L. Renfro
.
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- From: Dave L. Renfro
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- Re: 3435 = 3^3 + 4^4 + 3^3 + 5^5
- From: Dave L. Renfro
- Re: 3435 = 3^3 + 4^4 + 3^3 + 5^5
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- 3435 = 3^3 + 4^4 + 3^3 + 5^5
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