Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.

Let w < sub > j </ sub > be the ' price ' ( the rental ) of a certain factor j, let MP < sub > j1 </ sub > and MP < sub > j2 </ sub > be its marginal product in the production of goods 1 and 2, and let p < sub > 1 </ sub > and p < sub > 2 </ sub > be these goods ' prices.

Let the directrix be the line x = − p and let the focus be the point ( p, 0 ).

Let p, q > 2 be two distinct prime numbers.

Let p be an odd prime.

Let π < sub > 2 </ sub >( x ) denote the number of primes p ≤ x such that p + 2 is also prime.

Let X be a random variable with a discrete probability distribution p depending on a parameter θ.

Sylows ' test: Let n be a positive integer that is not prime, and let p be a prime divisor of n. If 1 is the only divisor of n that is equal to 1 modulo p, then there does not exist a simple group of order n.

# Let p = ( p < sub > 1 </ sub >, p < sub > 2 </ sub >) and q = ( q < sub > 1 </ sub >, q < sub > 2 </ sub >) be elements of W, that is, points in the plane such that p < sub > 1 </ sub > = p < sub > 2 </ sub > and q < sub > 1 </ sub > = q < sub > 2 </ sub >.

# Let p = ( p < sub > 1 </ sub >, p < sub > 2 </ sub >) be an element of W, that is, a point in the plane such that p < sub > 1 </ sub > = p < sub > 2 </ sub >, and let c be a scalar in R. Then cp = ( cp < sub > 1 </ sub >, cp < sub > 2 </ sub >); since p < sub > 1 </ sub > = p < sub > 2 </ sub >, then cp < sub > 1 </ sub > = cp < sub > 2 </ sub >, so cp is an element of W.

Let the open enemy to it be regarded as a Pandora with her box opened ; ;

Let every policeman and park guard keep his eye on John and Jane Doe, lest one piece of bread be placed undetected and one bird survive.

`` Let him be now ''!!

Let us assume that it would be possible for an enemy to create an aerosol of the causative agent of epidemic typhus ( Rickettsia prowazwki ) over City A and that a large number of cases of typhus fever resulted therefrom.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let Af be the null space of Af.

Let N be a linear operator on the vector space V.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.

Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.

Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.

Let us take a set of circumstances in which I happen to be interested on the legislative side and in which I think every one of us might naturally make such a statement.

Let the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.

Let this be denoted by Af.

Let it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.

Let not your heart be troubled, neither let it be afraid ''.

The same God who called this world into being when He said: `` Let there be light ''!!

For those who put their trust in Him He still says every day again: `` Let there be light ''!!

Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.

Let her out, let her out -- that would be the solution, wouldn't it??

Let p be an odd prime and a an integer coprime to p. Then

Given an integer n, choose some integer a < n. Let 2 < sup > s </ sup > d = n − 1 where d is odd.

Let p be an odd prime.

Let M < sub > p </ sub > = 2 < sup > p </ sup > − 1 be the Mersenne number to test with p an odd prime ( because p is exponentially smaller than M < sub > p </ sub >, we can use a simple algorithm like trial division for establishing its primality ).

Let p be an odd prime and let.

Let p be an odd prime number and a an integer.

Let G be a cycle graph of odd length greater than three ( a so-called " odd hole ").

Let there be given an ( n | n ) supermanifold with an odd Poisson bi-vector and a Berezin volume density, also known as a P-structure and an S-structure, respectively.

He wrote, " Let him mend his pen, get a bottle of visible ink, come out from the Old Manse, cut Mr. Alcott, hang ( if possible ), the editor of ' The Dial ,' and throw out of the window to the pigs all his odd numbers of the North American Review.

Let be a real-graded vector space equipped with a nonsingular antisymmetric bilinear superform ( i. e. ) such that is real if either or is an even element and imaginary if both of them are odd.

* Let there be n players, where n is odd.

Scalar multiplication for supermatrices is different than the ungraded case due to the presence of odd elements in R. Let X be a supermatrix.