math.hawaii.eduyuen/putnam-2016-questions.pdffind the smallest positive integer j such that for...

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Page 1: math.hawaii.eduyuen/Putnam-2016-questions.pdfFind the smallest positive integer j such that for every polynomial p(x) with integer coefficients and for every integer k, the integer
Page 2: math.hawaii.eduyuen/Putnam-2016-questions.pdfFind the smallest positive integer j such that for every polynomial p(x) with integer coefficients and for every integer k, the integer
Page 3: math.hawaii.eduyuen/Putnam-2016-questions.pdfFind the smallest positive integer j such that for every polynomial p(x) with integer coefficients and for every integer k, the integer
Page 4: math.hawaii.eduyuen/Putnam-2016-questions.pdfFind the smallest positive integer j such that for every polynomial p(x) with integer coefficients and for every integer k, the integer
Page 5: math.hawaii.eduyuen/Putnam-2016-questions.pdfFind the smallest positive integer j such that for every polynomial p(x) with integer coefficients and for every integer k, the integer
Page 6: math.hawaii.eduyuen/Putnam-2016-questions.pdfFind the smallest positive integer j such that for every polynomial p(x) with integer coefficients and for every integer k, the integer
Page 7: math.hawaii.eduyuen/Putnam-2016-questions.pdfFind the smallest positive integer j such that for every polynomial p(x) with integer coefficients and for every integer k, the integer
Page 8: math.hawaii.eduyuen/Putnam-2016-questions.pdfFind the smallest positive integer j such that for every polynomial p(x) with integer coefficients and for every integer k, the integer
Page 9: math.hawaii.eduyuen/Putnam-2016-questions.pdfFind the smallest positive integer j such that for every polynomial p(x) with integer coefficients and for every integer k, the integer
Page 10: math.hawaii.eduyuen/Putnam-2016-questions.pdfFind the smallest positive integer j such that for every polynomial p(x) with integer coefficients and for every integer k, the integer
Page 11: math.hawaii.eduyuen/Putnam-2016-questions.pdfFind the smallest positive integer j such that for every polynomial p(x) with integer coefficients and for every integer k, the integer
Page 12: math.hawaii.eduyuen/Putnam-2016-questions.pdfFind the smallest positive integer j such that for every polynomial p(x) with integer coefficients and for every integer k, the integer