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 Apr 17 revised How to show certain things related to scalar products removed unnecessary ">" caused by blockquote formatting Apr 17 accepted How to show certain things related to scalar products Apr 17 comment How to show certain things related to scalar products thank you for this answer Apr 17 comment How to show certain things related to scalar products thanks for all your help Apr 17 comment How to show certain things related to scalar products Thank you for this answer. I think I should be able to manage (3) now. With the geometric interpretation I am still a bit stuck. When you mention those 4 corners of the parallelogram, is each one an ordered pair, like $u= (u_1,u_2)$? Also, is "Pythagoras" written in the problem as a pointer to use the Pythagorean theorem somehow? I just don't know exactly where to apply it, I try to 'extend' the parallelogram horizontally to form right angles, but then the lengths become unclear... Apr 17 revised How to show certain things related to scalar products added 143 characters in body Apr 17 comment How to show certain things related to scalar products @Theo: yeah that was the 'workaround' I was trying out, but now I can go ahead and replace the alphas thanks to what you just taught me. Apr 17 revised How to show certain things related to scalar products added 2 characters in body Apr 17 comment How to show certain things related to scalar products @Theo: thank you so much for that! I was trying to figure out why it was such a mess... definitely valuable remarks! Apr 17 revised How to show certain things related to scalar products added 6 characters in body; added 114 characters in body; added 1 characters in body Apr 17 asked How to show certain things related to scalar products Apr 17 comment Subtraction and division with integers modulo 3 @Gerry: thanks for the explanation. I had copied that notation from Paul R. Halmos -Linear Algebra Problem Book... But, yeah I will definitely try to avoid using those sorts of fractions in the future. Apr 17 accepted How do you show this property of a differentiable function given information about the derivative? Apr 17 comment Subtraction and division with integers modulo 3 Thank you for this answer Apr 17 comment Subtraction and division with integers modulo 3 @Fabian: thanks for the helpful tips Apr 17 accepted Subtraction and division with integers modulo 3 Apr 17 comment Subtraction and division with integers modulo 3 @quanta: I'm sorry if I'm just completely missing something here, but are you saying there is a problem with the way I am trying to write down/express an idea, or with the idea itself that I am trying to carry out division on the integers modulo 5? Apr 17 comment Subtraction and division with integers modulo 3 @quanta: ok, yeah I meant by that 3 divided by 4 in integers modulo 5 (and I realize the way I used $x$ in my above comment was nonsense). But isn't that how you would carry out division of 3 by 4 in integers modulo 5? Since $4$ is the inverse of $4$, $3*4^{-1}=2$ in integers modulo 5, no? Apr 17 comment Subtraction and division with integers modulo 3 @quanta: thank you for the answer. I'm still digesting it, but I wanted to check if I am understanding part of the idea. If I wanted to divide on say integers modulo 5 (where there are a couple more examples) then for say $\frac{3}{4}=x$ I would first always calculate $4^{-1}$ and then multiply? And because of the gcd stuff you showed, I know that $1\equiv 4x \mod 5 \Rightarrow x = 4 \Rightarrow \frac{3}{4} = 2$? So in these cases it is about finding the inverses first? Apr 17 asked Subtraction and division with integers modulo 3