Is there any easy method to figure out if there is any solution to an equation like the following one:
$ a^2+b^2=123$
what is the method when the power is a natural number greater than 2(eg 3,4)?
Need solutions...
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Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Last edited by Labib on Thu Dec 16, 2010 10:44 pm, edited 1 time in total.
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Re: Need solutions...
ami latex lekhar cheshta korsi. but amar lekha ta latex style e dekhasse na kno?? :'(
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Re: Need solutions...
তুমি এইটাকে বোল্ড করে কালার চেঞ্জ করছ এই কারণে...
a^2+b^2=123$=a^2+b^2=123 $
আর ল্যাটেক চেক করার জন্য টেস্ট ফোরাম ব্যবহার করতে পার।
a^2+b^2=123$=a^2+b^2=123 $
আর ল্যাটেক চেক করার জন্য টেস্ট ফোরাম ব্যবহার করতে পার।
"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.
Re: Need solutions...
let $n$ be any integer then ..............
$n^2\equiv 0 or 1 \pmod {4}$
so $a^2+b^2\equiv 2or 0\pmod{4}$
but . $123\equiv 3\pmod{4}$ which contradicts with the original equation .
so there is no solution
$n^2\equiv 0 or 1 \pmod {4}$
so $a^2+b^2\equiv 2or 0\pmod{4}$
but . $123\equiv 3\pmod{4}$ which contradicts with the original equation .
so there is no solution
Re: Need solutions...
$a^2+b^2=0,1,2 \pmod{4}$ (you missed $1$)
"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.
Re: Need solutions...
thanks moon bhaya .i forgot about that , when one can be odd and other one is even