B. Show that 4n+ 4n+1 + 4n+2 + 4n+3 + 4n+4 is divisible by 11 for any positive integer n. C. Find the possible values of a so that an + an+1 + an+2 +an+3 + an+4 will be divisible by 11.

Q: Find the number zeroes with which the decimal representation of 700! terminates. a (a) 245 O (b) 199…

A: The objective is to find the number of zeroes with which the decimal representation of 700!…

Q: In Z6, evaluate the following expressions. > > V 3- (2 × 5) 3² +4² 5+3 2 × 3 1. 1 2. 2 3. 3 4. 4 5.…

A:

Q: Find the least common multiple and greatest common divisor o following algebraic expressions: 1.-…

A: Given: The algebraic expressions are:           1. a2b2c; ab2c2; a2bc3           2. x2y2z;…

Q: Let a be an odd integer. Show that (i) 8 | a2 − 1; (ii) 16 | a4 + 15.

A:

Q: If mis odd, then m3 - mis divisible by 3.

A: We will check this for m=1 first  0 is divisible  by 3.

Q: Find top and bottom elements of N0 with operation as division

A:

Q: Let a and b be integers, such that: a + 5b and: 5a - b, are both divisible by 2002. Try that; a² is…

A:

Q: Find the coefficient for the term afb5 from the expansion of: (3a - 2b)¹1 Answer:

A: We need to find the coefficient of a6b5 in the expansion of:(3a-2b)11

Q: if A and B are not dis joint than event, p(A Or B) LP (A) + PlB) True False

A: We have to find true or false.

Q: Simplify: 2n + Sn

A: Given,          2n+5n

Q: Find the product 3/2 (5 /12 + 6/6) and express your answer in the form A/B+ CVD, A, B, C, and D are…

A: Given : 32512 + 66

Q: The number 42 has the prime factorization 2- 3-7. Thus, 42 can be written in four ways as a product…

A: Factorise  910 inti prine factors and the find the required pairs.

Q: a) 5+3+1+(-1) ++ (-33)

A:

Q: 1+1+5215+5102

A:

Q: V2+Tt is an integer number * O True O False

A: Answer: False.

Q: The letter a is a digit (i.e., 0; 1; ; 9). Find all choices of n so that 278n5 is divisible by

A:

Q: = 5 Find a3, a4, and as for the recursive formula an = an-1 +3an-2 if a1 = 2 and a2

A: given   recursive formula is an= an-1+3an-2and   a1=2   ,  a2=5then we have to find  a3 , a4  , a5…

Q: what is 4ab+56ab+34ab2

A: We add like terms and take common then we get answer

Q: 26 + 4 × [9 - (1 + 4)

A: Given that  26 + 4 × [9 - (1 + 4)] To simplify the expression

Q: The product of any integer and 2 is greater than 2.

A:

Q: If (3n+2)! An? + Bn + C (3n)! determine the integer values of A, B, and C.

A:

Q: Let q and 7 be the quotient and remainder, respectively, of 19 divided by 9. What is does q + r…

A: Given that q and r are the quotient and remainder respectively of 19 divided by 9. Since we can…

Q: What is the greatest common divisor of 24 and 44? n If n is a natural number such that gcd(800, n) =…

A:

Q: Kathy's second card tells her to go back three steps. What integer represents her move back?

A:

Q: Consider the expression: x² - 7x - 30 = 30 and A) Find two number, p and q such that p. q p+q= - 7.…

A:

Q: (d) an 10"+1 +3 x 4"-1+5 is divisible by 9 for all n2 1,

A:

Q: Show that if 9 | a3 + b3 + c3 then 3 divides at least one of the integers a, b, or c.

A:

Q: |(8) Multiply in the indicated base 32 43seven b. x 6seven

A: Multiplication madlo

Q: Ans: Find the remainder (smallest nonnegative integer) when 1015!-1010! is divided by 1013-

A:

Q: Зх — 8 If 3 3 = 0, then x = ? 3 3 Зх — 8 3 3 Зх — 8 -7 6 -4 1 Find the product: 1 -4 3 1 1 1 1 1 1…

A:

Q: Evaluate this factorial expression: 6! -3!

A: factorial expression: 6! -3!

Q: 4503 is divisible by 2,3,,5,6,9or 10

A: 4503 is divisible by 2, 3, 5, 6, 9 or 10.