Difference between revisions of "1971 Canadian MO Problems/Problem 5"
(Created page with "<math>p(0)=a_nx^{n}+a_{n-1}x^{n-1}+...a_1x+a_0=a_0</math> We know that p(0) is odd, so we know <math>a_0</math> is odd. By Vieta's this means that all the roots of polynomial p...") |
(I LEAVE THIS PROBLEM OPEN. COME SOLVE IT.) |
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| − | <math>p( | + | == Problem == |
| + | Let <math>p(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x+a_0</math>, where the coefficients <math> a_i</math> are integers. If <math>p(0)</math> and <math>p(1)</math> are both odd, show that <math>p(x)</math> has no integral roots. | ||
| − | + | == Solution == | |
| + | {{solution}} | ||
| − | + | == See Also == | |
| − | + | [[Category:Intermediate Algebra Problems]] | |
| − | |||
| − | |||
Revision as of 15:52, 12 September 2012
Problem
Let 
, where the coefficients 
are integers. If 
and 
are both odd, show that 
has no integral roots.
Solution
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