tag:blogger.com,1999:blog-2400513859305780710.post1943997336251034183..comments2023-04-04T07:53:53.789-07:00Comments on Mathematical Food For Thought: It Only Matters In The End. Topic: Number Theory. Level: Olympiad.Jeffrey Wanghttp://www.blogger.com/profile/11114458640271201663noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-2400513859305780710.post-21126872871365532232009-12-30T11:17:10.000-08:002009-12-30T11:17:10.000-08:0010^2006 mod 252=100 * 1000^(2004/3) mod 252=100 * ...10^2006 mod 252=<br>100 * 1000^(2004/3) mod 252=<br>100 * (-8)^(2004/3) mod 252=<br>25 * (-2)^2006 mod 252=<br>25 * 4^1003 mod 252<br><br>but note that 4^4 = 4 mod 252 so this becomes<br>25 * 4^3 mod 252=<br>1600 mod 252=<br>88 mod 252. ...I think.morinhuurnoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-35420904023167540152009-12-30T11:54:45.000-08:002009-12-30T11:54:45.000-08:00Oh wait, 4^1003 then reduces to 4, not 4^3. Which...Oh wait, 4^1003 then reduces to 4, not 4^3. Which means it's 100 mod 252.morinhuurnoreply@blogger.com