How to solve f (x ) = g (y )...
... It turns out that: d is a congruent number if, and only if, the elliptic curve Ed : y 2 = x 3 − d 2 x has a solution with y 6= 0. In fact, a2 + b 2 = c 2 , 21 ab = d implies bd/(c − a), 2d 2 /(c − a) is a rational solution of y 2 = x 3 − d 2 x. Conversely, a rational solution of y 2 = x 3 − d 2 x wi ...
... It turns out that: d is a congruent number if, and only if, the elliptic curve Ed : y 2 = x 3 − d 2 x has a solution with y 6= 0. In fact, a2 + b 2 = c 2 , 21 ab = d implies bd/(c − a), 2d 2 /(c − a) is a rational solution of y 2 = x 3 − d 2 x. Conversely, a rational solution of y 2 = x 3 − d 2 x wi ...
CHAPTER 3: Cyclic Codes
... IV054 Hamming codes as cyclic codes Definition (Again!) Let r be a positive integer and let H be an r * (2r -1) matrix whose columns are distinct non-zero vectors of V(r,2). Then the code having H as its parity-check matrix is called binary Hamming code denoted by Ham (r,2). It can be shown that bi ...
... IV054 Hamming codes as cyclic codes Definition (Again!) Let r be a positive integer and let H be an r * (2r -1) matrix whose columns are distinct non-zero vectors of V(r,2). Then the code having H as its parity-check matrix is called binary Hamming code denoted by Ham (r,2). It can be shown that bi ...
