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#1 2007-10-16 10:49:00
- bossk171
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- Registered: 2007-07-16
- Posts: 305
I'm thinking of a number...
Actually, I'm thinking of three numbers:
a,b and c are three consecutive numbers. a is prime, b is a perfect cube, c is a perfect square. What is a?
The answer would be good, props to proving that there's only one answer though.
Use Hide tags.
EDIT: I made a huge mistake when I posted this. It's fixed now. SORRY.
Last edited by bossk171 (2007-10-16 14:03:21)
There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.
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#2 2007-10-17 00:22:58
- landof+
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Re: I'm thinking of a number...
simple, the orders give it all away, they must be close, good puzzle!
I shall be on leave until I say so...
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#3 2007-10-17 03:57:53
- bossk171
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Re: I'm thinking of a number...
landof+ is correct of course, does any one want to show that those are the only values for a, b, and c?
There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.
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#4 2007-10-17 04:29:14
- JaneFairfax
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Re: I'm thinking of a number...
I can prove that Landofs solution is the only solution provided I assume that no triangle number greater than 1 is a perfect cube. (A triangle number is a number N of the form N = 1+2+ +k for some natural number k.) I dont know how to verify that one, though.
Last edited by JaneFairfax (2007-10-17 04:38:26)
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#5 2007-10-17 05:34:59
- bossk171
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- Posts: 305
Re: I'm thinking of a number...
My proof was really, really, flawed, does someone have one that works?
landof+ can you post your answer? JaineFairfax, I'd like to see your proof too.
Last edited by bossk171 (2007-10-17 05:48:08)
There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.
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#6 2007-10-17 06:01:34
- JaneFairfax
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- Registered: 2007-02-23
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Re: I'm thinking of a number...
Last edited by JaneFairfax (2007-10-17 06:23:29)
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#7 2007-10-17 06:26:40
- bossk171
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Re: I'm thinking of a number...
this site confirms your suspicion that no triangle greater than one is a perfect squre but doesn't offer a proof
There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.
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#8 2007-10-17 22:03:27
- landof+
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- Posts: 131
Re: I'm thinking of a number...
my answer? a is 7.
In my opinion, I think it isn't the only solution. way beyond...
and you see...
p: 2,3,5,7,11,13,17,19,23.....
n^2: 1,4,9,16,25,36,49,64,81,100...
n^3: 1,8,27,64,125,216,343,512,729,1000.....
n^3 gets to (n-1)^2 and (n-2)^2 and so on, so it may be possible for another set.
I shall be on leave until I say so...
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#9 2007-10-18 03:07:18
- bossk171
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Re: I'm thinking of a number...
I disagree londof+, I thing JaneFairfax's proof kind of kills any chance of another answer.
There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.
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#10 2007-10-18 03:11:40
- JaneFairfax
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Re: I'm thinking of a number...
ARGHHH! The answer is staring us in the face all along. We are all blind.
b is a positive perfect cube, so
But a is prime; therefore one of the factors must be equal to 1. This cant be
, because n > 0.Offline
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