The 2-adic Valuation of the Coefficients of a Polynomial
نویسندگان
چکیده
from which it follows that dl(m) is a rational number with only a power of 2 in its denominator. Extensive calculations have shown that, with rare exceptions, the numerators of dl(m) contain a single large prime divisor and its remaining factors are very small. For example d6(30) = 2 12 · 7 · 11 · 13 · 17 · 31 · 37 · 639324594880985776531. Similarly, d10(200) has 197 digits with a prime factor of length 137 and its second largest divisor is 797. This observation lead us to investigate the arithmetic properties of dl(m). In this paper we discuss the 2-adic valuation of these dl(m). The fact that the coefficients of Pm(a) are positive is less elementary. This follows from a hypergeometric representation of N0,4(a;m) that implies the expression dl(m) = 2 −2m m
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