#Question Based On Division Algorithm

18 messages · Page 1 of 1 (latest)

loud mapleBOT
velvet meadow
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The reason that dividing by 4 is a common trick dealing with squares is that n^2 is either 0 or 1 mod 4 for a natural number n. Since 11 is clearly 3 mod 4 this solves the problem immediately. Here it is not helpful to note that all terms are odd as you can't conclude a lot from this besides the fact that IF a natural root existed it would have to be odd, too

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Looks like the only thing you have shown is that the square of an odd number is odd. That's a different result from what you are trying to show

unreal jungle
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Hello Sir, thanks for your helping hand. Can You please solve the problem like I solved? Our syllabus does not have number theory so I can’t understand very clearly what you’re talking about. Hope You understand 🙂

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I can send you the solution our teacher provided and based on that you can explain to me, if it is comfortable to You. Number Theory isn’t explicitly mentioned in our syllabus, so we were taught division algorithm to solve this problem.

velvet meadow
unreal jungle
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Okay Sir.

velvet meadow
# unreal jungle Okay Sir.

Can you explain to me please what you don't understand exactly in my reply? Just to make sure, where you need further explanation

unreal jungle
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Mod. And from “here it not helpful…..it would have to be odd.”

velvet meadow
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Ok, mod 4 is just a short writing. Every number that is r mod 4 can be written as 4k+r

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Like odd numbers are by definition just 1 mod 2

unreal jungle
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Our teacher divided every term by 4, and concluded that all of terms are of the type 4m+3 but perfect squares are of the form 4k or, 4k+1 but every terms present in sequence are of the form 4k+3 so there are no perfect squares present.

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Oh. Okay Sir.

velvet meadow
velvet meadow
unreal jungle
unreal jungle
unreal jungle
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This post was deleted mistakenly by me. Very sorry about that.