where the [p.sub.i] are the distinct

prime factors of N.

Secondly, we estimate the counting function of the set of square free positive integers having prime divisors that, when shifted, share a large common

prime factor. Both questions are motivated by a technique used in [3] to bound from below the degree of the field of coefficients of newforms in terms of the level.

Anyhow every

prime factor of an odd number which each * at the right of [J.sub.x] expresses is greater than [J.sub.x].

The range of accommodation, from five-star hotels to holiday apartments, was a

prime factor.

The growing global competition in which knowledge is a

prime factor for economic growth is increasingly shaping policies and setting the agenda for the future of European higher education.

The respondents were asked to identify the top three factors from the following list in terms of (1)

prime factor, (2) second

prime factor, and (3) encouraging factor.

Her coverage of fast algorithms includes index mapping and mixed-radix FFTs, Knonecker product factorization and FFTs, the family of

prime factor FFT algorithms, and computing the DFT of large prime length.

Let n be a positive large enough, if a

prime factor p of n!

They report in the online journal Nature Geoscience that increases in sea surface temperatures are not the

prime factor in producing monster storms such as Hurricane Katrina.

Bank of Ireland's chief economist Dan McLaughlin said: "The

prime factor behind this cyclical slowdown is falling residential construction.

Along with positive discrimination, it's the

prime factor in this country becoming an overflowing, third world sewer.