DIVISION OF INTEGERS

Let S be the set of integers which are divisible by 5, and let T be the set of integer which are divisible by 7. Find the number of positive integers less than 1000 and not in (S uu T) .

Let P(x) be a non-zero polynomial with integer coefficients.If P(n) is divisible for each positive integer n, what is the vale of P(0)?

Integers are closed under division.

If m and n are integers divisible by 5,which of the following is not necessarily true? m+n backslash is divisible by 10 (b) m-n is divisible by 5m^(2)-n^(2) is divisible by 25 (d) None lof these

List all possible multiplication and division statements for the integers with 5, –5, 6, –6 and 30, –30. For example, 5 × 6 = 30 .

" If "n" is positive integer then "2.4^(2n+1)+3^(3n+1)" is always divisible by a positive integer whose values is "lambda" then "lambda-2=

Theorem 1.1 (Euclid’s Division Lemma) : Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r leq b.

If n is an integer, then (n^(3) - n) is always divisible by :