Today I had my last lecture for number theory. But after that I feel so lazy. I am not sure what is the reason! Yesterday, I took some photos. However, my hands are shaky so the photos turned out to be very ugly. Nevertheless, I will post some of them here for criticising! (especially by ALEX).
Okay, thats about for photos. I should talk something about number theory today. In all, for this course, I have 65 theorems, lemmas, corollary in total. So obviously, to end the course, it will defintely be a theorem!!! So whats so 'big' about theorem 65? Basically, we learnt continued fractions and Pell's equation. Theorem 65 is the link between them. Consider the equation x^2 - dy^2 = 1, where d is a non square integer. Basically, this theorem says that if p_n and q_n are the convergents of the sqrt(d) then (x,y)=(p_n,q_n) are the solutions of the equation given certain conditions. First, n=lm-1 where l is a natural number and m is the period of the continued fraction of sqrt(d) and n must be an odd number. Seems complicated? Defintely not. Its fun! If you are feeling bored or nothing to do... maybe this can replace your sudoku puzzle when its so common nowadays. I am assure you that its more enjoyable than sudoku. To give yourself the fullest satisfaction, I will recommend you to prove this statement.
Anyway I got this friend who says that 'Life is short, make a fool of it while you can'. I will rephrase it... ' Life is short, make yourself and your family happy while you can and learn more mathematics too'!
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