| | [SOLVED] Funny squares |  |
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Bruno
Admin
Posts : 184
Join date : 2009-09-15
Age : 36
Location : the infinite, frictionless plane of uniform density
| | Subject: [SOLVED] Funny squares Tue Nov 17, 2009 10:00 pm | |
| This problem is my own. I hope you like it.  An integer is called base b funny if its base-b representation consists of the concatenated digits of two consecutive squares. For instance, 2536 is funny in base 10. A (base b) funny square is a square which is funny in base b. For instance 49 is a funny square in base 10 (and the only one I found up to 10^8 ). Show that there are no funny squares in base b if b is a square.
Last edited by Bruno on Wed Nov 25, 2009 11:56 am; edited 1 time in total | |
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Mohammad
Descartes
Posts : 100
Join date : 2009-11-05
Age : 40
Location : Right behind you
| | Subject: Re: [SOLVED] Funny squares Wed Nov 18, 2009 10:51 pm | |
| These numbers are really funny I start laughing at them now still. I will give a thought to it soon  | |
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peyman
Euclid
Posts : 49
Join date : 2009-11-06
Age : 100
Location : dense in the universe
| | Subject: Re: [SOLVED] Funny squares Wed Nov 18, 2009 10:55 pm | |
| they are funny and they even have a funny name!  | |
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Bruno
Admin
Posts : 184
Join date : 2009-09-15
Age : 36
Location : the infinite, frictionless plane of uniform density
| | Subject: Re: [SOLVED] Funny squares Wed Nov 18, 2009 10:56 pm | |
| Haha, you said "funny" twice!  | |
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peyman
Euclid
Posts : 49
Join date : 2009-11-06
Age : 100
Location : dense in the universe
| | Subject: Re: [SOLVED] Funny squares Tue Nov 24, 2009 11:10 pm | |
| Can you post your solution? | |
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Bruno
Admin
Posts : 184
Join date : 2009-09-15
Age : 36
Location : the infinite, frictionless plane of uniform density
| | Subject: Re: [SOLVED] Funny squares Tue Nov 24, 2009 11:33 pm | |
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Bruno
Admin
Posts : 184
Join date : 2009-09-15
Age : 36
Location : the infinite, frictionless plane of uniform density
| | Subject: Re: [SOLVED] Funny squares Wed Nov 25, 2009 2:41 am | |
| Nobody likes it?  | |
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peyman
Euclid
Posts : 49
Join date : 2009-11-06
Age : 100
Location : dense in the universe
| | Subject: Re: [SOLVED] Funny squares Wed Nov 25, 2009 9:21 am | |
| It's beautiful Bruno! I like it very much:  | |
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Mohammad
Descartes
Posts : 100
Join date : 2009-11-05
Age : 40
Location : Right behind you
| | Subject: Re: [SOLVED] Funny squares Wed Nov 25, 2009 11:41 am | |
| Nice solution, I am sure I couldn't solve it even if I was back in 20... Good job!  | |
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Bruno
Admin
Posts : 184
Join date : 2009-09-15
Age : 36
Location : the infinite, frictionless plane of uniform density
| | Subject: Re: [SOLVED] Funny squares Wed Nov 25, 2009 11:42 am | |
|  Thank you both. | |
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| | [SOLVED] Funny squares | |
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