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Topic: Challenging Problems
Replies: 1   Last Post: Nov 17, 1996 6:25 PM

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Walter Lee

Posts: 2
Registered: 12/6/04
Challenging Problems
Posted: Nov 15, 1996 11:27 PM
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Here are the problems: please respond before Tuesday, November 19, 1996 if
you know any of these answers. Thanks in advance.

1) 264² = 69696 and 2285² = 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
(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.

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