SOLUTIONS OF SOME CLASSES OF CONGRUENCES Eugen
... Proof. The proof of Proposition 2 is given by the following chain of formulas: xkl ≡ al (mod p), xkl+2 ≡ x2 al (mod p), x2 al ≡ 1 (mod p), x2 ≡ a−l (mod p). Actually, xkl+2 ≡ 1 (mod p) by Fermat theorem. If (5) has a solution, then it has two solutions. It is necessary to check whether they are the ...
... Proof. The proof of Proposition 2 is given by the following chain of formulas: xkl ≡ al (mod p), xkl+2 ≡ x2 al (mod p), x2 al ≡ 1 (mod p), x2 ≡ a−l (mod p). Actually, xkl+2 ≡ 1 (mod p) by Fermat theorem. If (5) has a solution, then it has two solutions. It is necessary to check whether they are the ...
A family of simple Lie algebras in characteristic two
... should be satisfied for every values of 2 F? , f g, which cannot occur. Then the only possible non-zero values can be assumed for (e(0; ) ; e(1; ) ): the sole ...
... should be satisfied for every values of 2 F? , f g, which cannot occur. Then the only possible non-zero values can be assumed for (e(0; ) ; e(1; ) ): the sole ...
164 B—B- T = H2+H\`B, and H2- C = 0, contrary to
... with integer rjij. Since the u{ are linearly independent in R, and con contains un, but no other co*, (i
... with integer rjij. Since the u{ are linearly independent in R, and con contains un, but no other co*, (i
translated mathematics style guide
... o For MSP, algorithms are generally NOT read to the student. o For EOC exams, algebraic expressions or equations are generally NOT read to the student. Replace with the phrase ‘…the equation(s) shown…’ or similar. • Absolute value o |4| is read as ‘the absolute value of 4’ • Trigonometry (EOC) o D ...
... o For MSP, algorithms are generally NOT read to the student. o For EOC exams, algebraic expressions or equations are generally NOT read to the student. Replace with the phrase ‘…the equation(s) shown…’ or similar. • Absolute value o |4| is read as ‘the absolute value of 4’ • Trigonometry (EOC) o D ...
Mark scheme - Solve My Maths
... mentioned. For this mark to be awarded a value between 169 and 171 inclusive must have been given as length of cupboard diagonal of Pythagoras' theorem used in calculating an incorrect length. ...
... mentioned. For this mark to be awarded a value between 169 and 171 inclusive must have been given as length of cupboard diagonal of Pythagoras' theorem used in calculating an incorrect length. ...
Solutions to Exercises, Section 1.1
... must have 5 appear once, and must have 9 appear once. The order of the rows in a table that define a function do not matter. For convenience, we put the first column in numerical order 3, 5, 9. Because the range must be {2, 4}, the second column must contain 2 and 4. There are three slots in which to ...
... must have 5 appear once, and must have 9 appear once. The order of the rows in a table that define a function do not matter. For convenience, we put the first column in numerical order 3, 5, 9. Because the range must be {2, 4}, the second column must contain 2 and 4. There are three slots in which to ...
Equation
In mathematics, an equation is an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions. An equation differs from an identity in that an equation is not necessarily true for all possible values of the variable.There are many types of equations, and they are found in all areas of mathematics; the techniques used to examine them differ according to their type.Algebra studies two main families of equations: polynomial equations and, among them, linear equations. Polynomial equations have the form P(X) = 0, where P is a polynomial. Linear equations have the form a(x) + b = 0, where a is a linear function and b is a vector. To solve them, one uses algorithmic or geometric techniques, coming from linear algebra or mathematical analysis. Changing the domain of a function can change the problem considerably. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory. These equations are difficult in general; one often searches just to find the existence or absence of a solution, and, if they exist, to count the number of solutions.Geometry uses equations to describe geometric figures. The objective is now different, as equations are used to describe geometric properties. In this context, there are two large families of equations, Cartesian equations and parametric equations.Differential equations are equations involving one or more functions and their derivatives. They are solved by finding an expression for the function that does not involve derivatives. Differential equations are used to model real-life processes in areas such as physics, chemistry, biology, and economics.The ""="" symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.