Examples of using Any positive integer in English and their translations into Bulgarian
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Ecclesiastic
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Computer
For any positive integer n.
Is divisible by for any positive integer. 3.
Let be any positive integer not equal to or.
(ii) Prove that does not divide for any positive integer. S 7.
Prove that for any positive integer there exists such that.
S 3 Let be positive integers such that for any positive integer we have.
Show that for any positive integers and, cannot be a power of.
There are given two arithmetical progressions and, such that for any positive integer, and have the same set of exponents.
For any positive integer, let denote the square of the sum of the digits of.
Prove that there doesn't exist any positive integer such that and are perfect squares. 2.
For any positive integer the sum is written in the form, where and are relatively prime.
Consider the sequence defined recursively by(any positive integer), and For which of the following values of must?
For any positive integer, let denote the number of different prime divisors of the number.
In other words a composite number is any positive integer greater than one that is not a prime number.
For any positive integer, let denote the number of ordered pairs of positive integers for which.
A positive integer has the property that for any positive integer which is co-prime with, we have.
S 3 For any positive integer, let denote the number of its positive divisors(including 1 and itself).
Let be given positive real number,find all the functions such that holds for any positive integers, satisfying.
Prove that for any positive integer, the number.
Any positive integer obtained by removing several(at least one) digits from the right-hand end of the decimal representation of is called a stump of.
Note that for any positive integer n, Γ(n)=(n- 1)!
For any positive integer, let be the number of elements in the set whose base 2 representation contains exactly three 1s.
A sequence is defined by Prove that for any positive integer we have(where[x] denotes the smallest integer x).
Given any positive integer, show that there exist distint positive integers and such that divides for;
Let and for j Prove that for any positive integer n the roots of the equation are all real and distinct.
For any positive integer, prove that there exists an-th degree polynomial with integer coefficients such that the numbers,,,….
Prove that there are infinitely many positive integers, such that is not prime for any positive integer.
Show that for any positive integer we can find such that is a multiple of.
(a) Prove that for any positive integer, there exists at least one positive integer such that.
Prove or disprove: For any positive integer there exists an integer such that the binomial coeffcient is divisible by for any. .