টামটা সংখ্যা

For discussing Olympiad Level Number Theory problems
MATHPRITOM
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টামটা সংখ্যা

Unread post by MATHPRITOM » Sat Feb 04, 2012 7:48 pm

প্রমাণ কর,চার অংকের কোন টামটা সংখ্যাই (palindrome number) perfect square নয় ।

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Phlembac Adib Hasan
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Re: টামটা সংখ্যা

Unread post by Phlembac Adib Hasan » Sat Feb 04, 2012 9:44 pm

Well,I'm giving here a less beautiful proof.(As I don't have time to find a nice one -tomorrow I have a Physics exam in pvt.)
\[(abba)_{10}=11(91a+10b)\] \[\Rightarrow 3a-b\equiv 0 (mod \; 11)\]Now we can put $9$ different values of $a$.Like for $a=1$,we find only $b=3$ follows the condition.But $1331=11^3$ is not a perfect square.For $a=2$, we find $b=6$ only.But $2662=2.11^3$ is not a perfect square.Checking the remaining $7$ cases, we find none of them is perfect square.So my proof is complete.
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