Significant Figures - Waterford Public Schools
... with only one digit to the left of the decimal point If the decimal point is moved to the left (number greater than 1), the exponent will be a positive number Example: If the decimal point is moved to the right (number less than 1), the exponent will be a negative number Example: ...
... with only one digit to the left of the decimal point If the decimal point is moved to the left (number greater than 1), the exponent will be a positive number Example: If the decimal point is moved to the right (number less than 1), the exponent will be a negative number Example: ...
Dismal Arithmetic
... (Corollary 8). These factorizations are in general not unique. There is a useful process using digit maps for “promoting” a prime from a lower base to a higher base, which enables us to replace the list of all primes by a shorter list of prime “templates” (Table 3). Dismal squares are briefly discu ...
... (Corollary 8). These factorizations are in general not unique. There is a useful process using digit maps for “promoting” a prime from a lower base to a higher base, which enables us to replace the list of all primes by a shorter list of prime “templates” (Table 3). Dismal squares are briefly discu ...
Least Common Multiple
... LCM is the smallest number other than 0 that is a multiple of 2 or more whole numbers ...
... LCM is the smallest number other than 0 that is a multiple of 2 or more whole numbers ...
Large gaps between consecutive prime numbers
... This is the route followed by all authors up to and including Rankin [29]; improvements to G(x) up to this point depended on improved bounds for counts of smooth numbers. The new idea introduced by Maier and Pomerance [24] was to make the third sieving more efficient (and less trivial!) by using man ...
... This is the route followed by all authors up to and including Rankin [29]; improvements to G(x) up to this point depended on improved bounds for counts of smooth numbers. The new idea introduced by Maier and Pomerance [24] was to make the third sieving more efficient (and less trivial!) by using man ...
2. Ideals in Quadratic Number Fields
... Note that if I and J are ideals in R, then so are I + J = {i + j : i ∈ I, j ∈ J}, IJ = {i1 j1 + . . . + in jn : i1 , . . . , in ∈ I, j1 , . . . , jn ∈ J}, as well as I ∩ J. The index n in the product IJ is meant to indicate that we only form finite sums. If A and B are ideals in some ring R, we say ...
... Note that if I and J are ideals in R, then so are I + J = {i + j : i ∈ I, j ∈ J}, IJ = {i1 j1 + . . . + in jn : i1 , . . . , in ∈ I, j1 , . . . , jn ∈ J}, as well as I ∩ J. The index n in the product IJ is meant to indicate that we only form finite sums. If A and B are ideals in some ring R, we say ...
PDF
... which is one more than 561 times 34628679005806222298029624007549356624641833138184305191654410155773 Hence 561 is an Euler pseudoprime. The next few Euler pseudoprimes to base 2 are 1105, 1729, 1905, 2047, 2465, 4033, 4681 (see A047713 in Sloane’s OEIS). An Euler pseudoprime is sometimes called an ...
... which is one more than 561 times 34628679005806222298029624007549356624641833138184305191654410155773 Hence 561 is an Euler pseudoprime. The next few Euler pseudoprimes to base 2 are 1105, 1729, 1905, 2047, 2465, 4033, 4681 (see A047713 in Sloane’s OEIS). An Euler pseudoprime is sometimes called an ...
Lecture notes, sections 2.1 to 2.3
... Theorem 8 (Bezout’s theorem). Let a, b ∈ Z. Then GCD(a, b) can be written as a linear combination of a and b. Proof. The previous theorem shows that GCD(a, b) is an element of ha, bi. Theorem 9. The intersection of two ideals is an ideal. (I forgot to prove this in class, but include it here for com ...
... Theorem 8 (Bezout’s theorem). Let a, b ∈ Z. Then GCD(a, b) can be written as a linear combination of a and b. Proof. The previous theorem shows that GCD(a, b) is an element of ha, bi. Theorem 9. The intersection of two ideals is an ideal. (I forgot to prove this in class, but include it here for com ...
