03 Oct 14
I am polishing off a book by mathematician Ian Stewart by reading the end notes. For brevity I'll leave out the last paragraph of the note. I use ^ for taking a power and sqt[ ] for square root.
"Introduce the norm
N(a + b sqt[15]) = a^2 - 15 b^2
which has the lovely property
N(xy) = N(x) N(y)
Then
N(2) = 4 N(5) = 25 N(5+sqt[15]) = 10 N(5-sqt[15]) = 10"
It seems to me that N(2) = 2^2 - 15 0^2 = 4, which is not 10. What am I doing wrong?
04 Oct 14
Originally posted by Paul Dirac IIAfter the "Then" there are four separate lines. It is not one line.
I am polishing off a book by mathematician Ian Stewart by reading the end notes. For brevity I'll leave out the last paragraph of the note. I use ^ for taking a power and sqt[ ] for square root.
"Introduce the norm
N(a + b sqt[15]) = a^2 - 15 b^2
which has the lovely property
N(xy) = N(x) N(y)
Then
N(2) = 4 N(5) = 25 N(5+sqt[15]) = 10 N ...[text shortened]... ]) = 10"
It seems to me that N(2) = 2^2 - 15 0^2 = 4, which is not 10. What am I doing wrong?
N(2) = 4
N(5) = 25
N(5+sqt[15]) = 10 because 5^2-1^2*15 = 10
N(5-sqt[15]) = 10 because 5^2-(-1)^2*15 = 10