tag:blogger.com,1999:blog-2400513859305780710.post1332776224265902037..comments2023-04-04T07:53:53.789-07:00Comments on Mathematical Food For Thought: Pick one, any one! Topic: Algebra. Level: OlympiadJeffrey Wanghttp://www.blogger.com/profile/11114458640271201663noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2400513859305780710.post-5066952195692921392005-12-30T21:02:06.000-08:002005-12-30T21:02:06.000-08:00Do you think you'll make it to MOSP this year?...Do you think you'll make it to MOSP this year?Mattnoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-34794185607828819172005-12-30T22:14:06.000-08:002005-12-30T22:14:06.000-08:00Well, that's my goal... I think I have a chanc...Well, that's my goal... I think I have a chance. Who are you?paladin8noreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-50985982811210472982005-12-31T12:44:31.000-08:002005-12-31T12:44:31.000-08:00I dont really know you at all, actually I found yo...I dont really know you at all, actually I found your blog on AOPS. It's actually been really helpful... thank you! I just noticed you were very proficient at these olympiad level problems and wondered if you that you're good enoguh yet to make MOSP.Mattnoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-47001413722415427052006-01-02T13:45:08.000-08:002006-01-02T13:45:08.000-08:00Go Jeffrey go! Yeah, he has a good chance of maki...Go Jeffrey go! Yeah, he has a good chance of making MOSP this year. <br><br>1. Setting y = 0 we get f(x^2) = x f(x), and setting x = 0 we get f(-y^2) = -y f(y) so we know f(x) is an odd function. If we desire to find the value of some f(a), we can write f(a) = a^{ \frac{1}{2}} f(a^{ \frac{1}{2}}) = a^{ \frac{1}{2} + \frac{1}{4} } f(a^{\frac{1}{4}) = ... the expression a^{ \frac{1}{2^{n}} } tends to 1, so we have f(a) = f(1) a for all integers. Thus, f(x) = mx for some constant m.QCnoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-16742816003547760552006-01-02T13:45:54.000-08:002006-01-02T13:45:54.000-08:00*for all reals*for all realsQCnoreply@blogger.com