Prove that no integer in the sequence
\[ 11,111,1111,11111, \cdots \]
is the square of an integer.
No square in a sequence
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AntiviruShahriar
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Re: No square in a sequence
~every square is the form of 4q or 4q+1.........
here 2^2=4.Nearest multiple of 4 to these numbers are _._._._._._._._08.And 11-08=3
so, 11_=3(mod4)
111_=3(mod4)
.
.................
so they are the form of 4q+3 and these are not square of integers...............
here 2^2=4.Nearest multiple of 4 to these numbers are _._._._._._._._08.And 11-08=3
so, 11_=3(mod4)
111_=3(mod4)
.
.................
so they are the form of 4q+3 and these are not square of integers...............
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kamrul2010
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Re: No square in a sequence
যে কোনো বিজোড় স্বাভাবিক সংখ্যাকে ৮ দ্বারা ভাগ করিলে ১ অবশষ্ট থাকে!! 
ইয়েস,কমন পড়সে!
ইয়েস,কমন পড়সে!
If computers have no doors or fences, who needs Windows and Gates?
Re: No square in a sequence
AntiviruShahriar wrote:
I am deleting both of these posts. PLEASE don't spam like this. It distracts people from the mail discussion. I hope you understand.Muhiminul Maruf wrote:
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.