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Challenging Problems
Posted:
Nov 15, 1996 11:27 PM


Here are the problems: please respond before Tuesday, November 19, 1996 if you know any of these answers. Thanks in advance.
1) 264ÃÂ² = 69696 and 2285ÃÂ² = 5221225
These numbers are palindromic numbers. Notice these planidromic numbers have a odd number of digits. Is there a number whose square is a palindromic number with an even number of digits?
2) 6a cc d ae 13c ff What is this? Who wrote it and to whom? 7i 3l 9n 4o 4qrr 4s 9t 12vx
3) What is a trinomial factor of x^11 + x^4 + 1?
4) 1/x + 1/(x+1) + 1/(x+2) + 1/(x+3) + 1/(x+4) = 0
This equation has 4 irrational roots. If all 4 roots lie in the interval a,b (that is: a<root 1<root 2<root 3<root 4<b), what are the smallest integral values of a and b?
Once again, any answers to these would be appreciated.



