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Topic: Take Non-Zero Decimal Digits, Get Square? (Read 296 times) |
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K Sengupta
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Take Non-Zero Decimal Digits, Get Square?
« on: Jul 27th, 2007, 8:01am » |
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Analytically determine whether any 9 digit decimal number that contains all the decimal digits except zero and does not end with 5 can be a perfect square.
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SMQ
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Re: Take Non-Zero Decimal Digits, Get Square
« Reply #1 on: Aug 14th, 2007, 6:00am » |
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I don't know about analytically, but empirically, yes, there are 30 of them.
--SMQ
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--SMQ
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Eigenray
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Re: Take Non-Zero Decimal Digits, Get Square
« Reply #2 on: Aug 14th, 2007, 9:32am » |
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But there are none that do end in 5:
If n2 ends in 5, then n=10k+5 for some k. But then n2 mod 1000 is either 025, 225, or 625 depending on the vaue of k mod 5. Since the first two are unacceptable, we find that k=2 mod 5. But in this case we find that n2 is either 0625 or 5625 mod 10000, which is no good.
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