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 p be an odd prime number.

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 ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.

Let denote the Bézier curve determined by the points P < sub > 0 </ sub >, P < sub > 1 </ sub >, ..., P < sub > n </ sub >.

Suppose that in a mathematical language L, it is possible to enumerate all of the defined numbers in L. Let this enumeration be defined by the function G: W → R, where G ( n ) is the real number described by the nth description in the sequence.

Let n be the number of points and d the number of dimensions.

Let X be a finite set with n elements.

Let A be the arithmetic mean and H be the harmonic mean of n positive real numbers.

Let n denote a complete set of ( discrete ) quantum numbers for specifying single-particle states ( for example, for the particle in a box problem we can take n to be the quantized wave vector of the wavefunction.

Let ε ( n ) denote the energy of a particle in state n. As the particles do not interact, the total energy of the system is the sum of the single-particle energies.

Let x < sub > 1 </ sub >, ..., x < sub > n </ sub > be the sizes of the heaps before a move, and y < sub > 1 </ sub >, ..., y < sub > n </ sub > the corresponding sizes after a move.

Let s = x < sub > 1 </ sub > ⊕ ... ⊕ x < sub > n </ sub > and t = y < sub > 1 </ sub > ⊕ ... ⊕ y < sub > n </ sub >.

Let n be the length of a statement in Presburger arithmetic.

Let ( q < sub > 1 </ sub >, w, x < sub > 1 </ sub > x < sub > 2 </ sub >... x < sub > m </ sub >) ( q < sub > 2 </ sub >, y < sub > 1 </ sub > y < sub > 2 </ sub >... y < sub > n </ sub >) be a transition of the GPDA

Let be an oriented smooth manifold of dimension n and let be an n-differential form that is compactly supported on.

:: Let n = 0

Let be a random sample of size n — that is, a sequence of independent and identically distributed random variables drawn from distributions of expected values given by µ and finite variances given by σ < sup > 2 </ sup >.

Let M be an n × n Hermitian matrix.

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

Let his bones and his memory rest in the fifteenth century where they belong ; ;

Let us quote once more from R. G. Collingwood: `` History is properly concerned with the actions of human beings Regarded from the outside, an action is an event or series of events occurring in the physical world ; ;

Let us therefore consider each of the three types of cost in turn, recognizing that this simplified classification is used only for illustrative purposes ; ;

Let Mullins keep the firm seat ; ;

Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord ; and the prayer of faith will save the sick man, and the Lord will raise him up ; and if he has committed sins, he will be forgiven.

Let S ( fig. 5 ) be any optical system, rays proceeding from an axis point O under an angle u1 will unite in the axis point O ' 1 ; and those under an angle u2 in the axis point O ' 2.

For a compilation album of the Glenmark duo Gemini, Andersson had Björn Ulvaeus write new Swedish lyrics for the re-recording of two old songs ; Ulvaeus also wrote new English lyrics to older Swedish language songs for opera singer Anne Sofie von Otter tribute album " I Let The Music Speak ".

The original posters showed Bennett himself ; a kindly looking old man offering guidance and support to would-be students with the phrase " Let me be your father " attached.

During the January 1969 sessions for the Let It Be album, the Beatles played a slow impromptu version of " Mailman, Bring Me No More Blues " — although not written by Holly, it was popularized by him — with Lennon mimicking Holly's vocal style ; the recording was eventually released in the mid-1990s on Anthology 3.

" Let there arise from you a group of people inviting to what is good, enjoining what is right, and forbidding what is wrong ; these are the ones who will be successful.

Let Marcion then exhibit, as gifts of his god, some prophets, such as have not spoken by human sense, but with the Spirit of God, such as have both predicted things to come, and have made manifest the secrets of the heart ; let him produce a psalm, a vision, a prayer -- only let it be by the Spirit, in an ecstasy, that is, in a rapture, whenever an interpretation of tongues has occurred to him ; let him show to me also, that any woman of boastful tongue in his community has ever prophesied from amongst those specially holy sisters of his.

Gloria Gaynor ( born September 7, 1949 ) is an American singer, best known for the disco era hits ; " I Will Survive " ( Hot 100 number 1, 1979 ), " Never Can Say Goodbye " ( Hot 100 number 9, 1974 ), " Let Me Know ( I Have a Right )" ( Hot 100 number 42, 1980 ) and " I Am What I Am " ( R & B number 82, 1983 ).

Let φ be a formula of degree k + 1 ; then we can write it as

Let now x ' and y ' be tuples of previously unused variables of the same length as x and y respectively, and let Q be a previously unused relation symbol which takes as many arguments as the sum of lengths of x and y ; we consider the formula

Before he died, Rabbeinu HaKadosh said: ‘ I need my sons !… Let the lamp continue to burn in its usual place ; let the table be set in its usual place ; let the bed be made in its usual place .” ( Kesubbos / Ketubot 103a )

' Let us obey the Biblical injunction: you of course, have the choice of natural means ; but as for me, I am afraid that there is no course open to me but the scientific way.