document.write( "Question 1182506: Let P(x) be a nonconstant polynomial, where all the coefficients are
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Algebra.Com's Answer #812594 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "when the degree is 1, P(x) = c1x+c2, certainly you can\r\n" );
document.write( "put in infinitely many positive integers for x and get a composite number.\r\n" );
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document.write( "For P(x) with degrees m > 1:\r\n" );
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document.write( "\"P%28x%29\"\"%22%22=%22%22\"\"sum%28c%5Bk%5D%28x%5Ek%29%2Ck=0%2Cm%29\", ci ≥ 0.\r\n" );
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document.write( "\"P%28a%29-P%28b%29\"\"%22%22=%22%22\"\"sum%28c%5Bk%5D%28a%5Ek%29%2Ck-0%2Cn%29-sum%28c%5Bk%5D%28b%5Ek%29%2Ck=0%2Cm%29\"\"%22%22=%22%22\"\"sum%28c%5Bk%5D%28a%5Ek-b%5Ek%29%2Ck=0%2Cm%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"sum%28c%5Bk%5D%28a-b%29sum%28a%5E%28k-1-j%29%2Ab%5Ej%2Cj=0%2Ck-1%29+%2Ck=0%2Cm%29\"\"%22%22=%22%22\"\"%28a-b%29sum%28c%5Bk%5Dsum%28a%5E%28k-1-j%29%2Ab%5Ej%2Cj=0%2Ck-1%29+%2Ck=0%2Cm%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"%28a-b%29%28matrix%281%2C8%2Cthe%2Csum%2Cof%2Ctwo%2C+or%2C+more%2Cpositive%2Cintegers%29%29\"\r\n" );
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document.write( "There are an infinite number of ways we can choose a and b a > b, such\r\n" );
document.write( "that a-b is not 1.  And the summation is of two or more positive integers,\r\n" );
document.write( "which are integers > 1. \r\n" );
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document.write( "So there exist infinitely many positive integers n such that P(n) is\r\n" );
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document.write( "Edwin
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