Chapter 1 Plane figurate numbers - Beck-Shop
... points on the plane, which forms a regular polygon. One speaks about m-gonal numbers if the arrangement forms a regular m-gon. 1.1.2. Polygonal numbers were a concern of Pythagorean Geometry, since Pythagoras is credited with initiating them, and originating the notion that these numbers are generat ...
... points on the plane, which forms a regular polygon. One speaks about m-gonal numbers if the arrangement forms a regular m-gon. 1.1.2. Polygonal numbers were a concern of Pythagorean Geometry, since Pythagoras is credited with initiating them, and originating the notion that these numbers are generat ...
THE DEVELOPMENT OF THE PRINCIPAL GENUS
... on to observe that the conjecture is only true in general when a and b are allowed to be rational numbers, and gives the example 89 = 4 · 22 + 1, which can be written as 89 = 11( 25 )2 + ( 92 )2 but not in the form 11a2 + b2 with integers a, b. Thus, he says, the theorem has to be formulated like th ...
... on to observe that the conjecture is only true in general when a and b are allowed to be rational numbers, and gives the example 89 = 4 · 22 + 1, which can be written as 89 = 11( 25 )2 + ( 92 )2 but not in the form 11a2 + b2 with integers a, b. Thus, he says, the theorem has to be formulated like th ...
A2-Level Maths: Core 3 for Edexcel
... Before looking at the multiplication and division of algebraic fractions, let’s recall the methods used for numerical fractions. ...
... Before looking at the multiplication and division of algebraic fractions, let’s recall the methods used for numerical fractions. ...
Rational Numbers
... • If the numerator and denominator of a rational number are multiplied or divided by a nonzero integer, we get a rational number which is said to be equivalent to the given rational number. • Rational numbers are classified as positive, zero or negative rational numbers. When the numerator and denom ...
... • If the numerator and denominator of a rational number are multiplied or divided by a nonzero integer, we get a rational number which is said to be equivalent to the given rational number. • Rational numbers are classified as positive, zero or negative rational numbers. When the numerator and denom ...
Logic and Proof - Numeracy Workshop
... The truth or falsity of a converse can not be inferred from the truth or falsity of the original statement. For example, x = 2 ⇒ x2 = 4 is true, but . . . its converse x2 = 4 ⇒ x = 2 is false, because x could be equal to −2. ...
... The truth or falsity of a converse can not be inferred from the truth or falsity of the original statement. For example, x = 2 ⇒ x2 = 4 is true, but . . . its converse x2 = 4 ⇒ x = 2 is false, because x could be equal to −2. ...
2ch2l9
... Equivalent Fractions 2-9 and Mixed Numbers In some recipes the amounts of ingredients are given as fractions, and sometimes those fractions do not equal the fractions on a measuring cup. Knowing how fractions relate to each other can be very helpful. Different fractions can name the same number. ...
... Equivalent Fractions 2-9 and Mixed Numbers In some recipes the amounts of ingredients are given as fractions, and sometimes those fractions do not equal the fractions on a measuring cup. Knowing how fractions relate to each other can be very helpful. Different fractions can name the same number. ...
Primes of the form x2 + ny2
... Furthermore, a monic integer polynomial fn (x) of degree h(−4n) satisfies above condition if and only if fn (x) is irreducible over Z, √ integer α, for which we have √ and is the minimal polynomial of a real algebraic L = K(α) where, K = Q( −n) and L is the ring class field of the order Z[ −n] in K. ...
... Furthermore, a monic integer polynomial fn (x) of degree h(−4n) satisfies above condition if and only if fn (x) is irreducible over Z, √ integer α, for which we have √ and is the minimal polynomial of a real algebraic L = K(α) where, K = Q( −n) and L is the ring class field of the order Z[ −n] in K. ...
Full text
... not divisible hyp is 2*13*24*3... rSr~l, where % is the number of I'S in the base p expansion of n. Proof: First, we note that the maximum exists. It is well known that rx
... not divisible hyp is 2*13*24*3... rSr~l, where % is the number of I'S in the base p expansion of n. Proof: First, we note that the maximum exists. It is well known that rx
1, so r < p +1. By Kummer's Theorem for Generalized Binomial Coefficients, /?|[£] g if ...
older, more formal version
... where there are m copies of Z/n. So the answer to our question is yes. However, this last step is not entirely satisfying, since we have just repeated the same group over and over again. We could instead ask if there are more interesting ways to obtain such a groupoid. For example, could we instead ...
... where there are m copies of Z/n. So the answer to our question is yes. However, this last step is not entirely satisfying, since we have just repeated the same group over and over again. We could instead ask if there are more interesting ways to obtain such a groupoid. For example, could we instead ...