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Many properties of a natural number n can be ... 30, 42, 66, 70, 78, 102, 105, 110, 114 ... Finding the prime factors is often harder than computing gcd and lcm using ...
42 is a pronic number, [1] an abundant number [2] as well as a highly abundant number, [3] a practical number, [4] an admirable number, [5] and a Catalan number. [6]The 42-sided tetracontadigon is the largest such regular polygon that can only tile a vertex alongside other regular polygons, without tiling the plane.
It can also be said that 42 is divisible by 7, 42 is a multiple of 7, 7 divides 42, or 7 is a factor of 42. The non-trivial divisors of 6 are 2, −2, 3, −3.
2.42 Perrin primes. 2.43 ... write the prime factorization of n in base 10 and concatenate the factors; iterate until a prime ... Many generalizations of Mersenne ...
If none of its prime factors are repeated, it is called squarefree. (All prime numbers and 1 are squarefree.) For example, 72 = 2 3 × 3 2, all the prime factors are repeated, so 72 is a powerful number. 42 = 2 × 3 × 7, none of the prime factors are repeated, so 42 is squarefree. Euler diagram of numbers under 100:
Many 19th century mathematicians still considered 1 to be prime, [42] and Derrick Norman Lehmer included 1 in his list of primes less than ten million published in 1914. [43] Lists of primes that included 1 continued to be published as recently as 1956.
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However, in this case, there is some fortuitous cancellation between the two factors of P n modulo 25, resulting in P 4k −1 ≡ 3 (mod 25). Combined with the fact that P 4 k −1 is a multiple of 8 whenever k > 1 , we have P 4 k −1 ≡ 128 (mod 200) and ends in 128, 328, 528, 728 or 928.