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31 cm = 3.1 dm – wingspan of largest butterfly species Ornithoptera alexandrae; 32 cm – length of the Goliath frog, the world's largest frog; 46 cm = 4.6 dm – length of an average domestic cat; 50 to 65 cm = 5–6.5 dm – a coati's tail; 66 cm = 6.6 dm – length of the longest pine cones (produced by the sugar pine [117])
The polynomial x 2 + cx + d, where a + b = c and ab = d, can be factorized into (x + a)(x + b).. In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
But observe that if N had a subroot factor above =, Fermat's method would have found it already. Trial division would normally try up to 48,432; but after only four Fermat steps, we need only divide up to 47830, to find a factor or prove primality. This all suggests a combined factoring method.
Algorithm: SFF (Square-Free Factorization) Input: A monic polynomial f in F q [x] where q = p m Output: Square-free factorization of f R ← 1 # Make w be the product (without multiplicity) of all factors of f that have # multiplicity not divisible by p c ← gcd(f, f′) w ← f/c # Step 1: Identify all factors in w i ← 1 while w ≠ 1 do y ...
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For general-purpose factoring, ECM is the third-fastest known factoring method. The second-fastest is the multiple polynomial quadratic sieve, and the fastest is the general number field sieve. The Lenstra elliptic-curve factorization is named after Hendrik Lenstra.
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3M will start paying out its $12.5 billion "forever chemicals" settlement with public water systems later this year after a federal judge gave final approval to the deal last week. The settlement ...