If gcd(7, a) = 1, prove that either a +1 or a – 1 is divisible by 7. 20

Q: Determine the coefficient of xaxzx if (x1 + x2 + x3 + x4)1ª is expandec

A: This is given by the multinomial coefficient formula. We state the theorem and then deduce the…

Q: 10 a.) Completely simplify E ()2* i=0 b.) Expand (1 – r)® and simplify. c.) Expand (r +r-1)5 and…

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Q: How many elements are in Z5[i]/<1 + i>?

A: Given Data The expression is Z5[i]/<1+i>.   Consider the Z5[i]/<1+i> in the form of…

Q: Show that A8 contains an element of order 15.

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Q: Evaluate ak+2 if ap

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Q: Find x and y such that,  77815x - 8216y=(77815 , 8216

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Q: Find all integers x + 3 such that x – 3 is divisible by x – 3. |

A: To find all integers such that x^3-3 is divisible by x-3

Q: Find all (p, q, r) such that ((p + -4) evaluates to 1.

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Q: Indicate the least integer n such that (3x5 + x²)4 = 0(x¹). E

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Q: ndicate the least integer n for which (3x5 + x2)4 is O(xn).

A: Solved using the binomial theorem

Q: a) How can you find a linear combination (with integer coefficients) of two integers that equals…

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Q: Let an be recursively defined by a₁ n≥ 1. Find lim an. 84x = 3/4, an+1 = = n n+2 . a for

A: To find the limit of the sequence

Q: In each item, you are given a set of vectors S the vectors into the columns of a matrix A rref R of…

A: As per our guideline we are supposed to answer first three subparts.kindly repost other question.…

Q: Find the term of (a – 2b)3 that has b in it. |

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Q: Suppose that a and b are integers, c b = 3 (mod 19). Find the integer c that a) с%3D 13а (mod 19).…

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Q: If GCD of (a,b) is 1 we can find the lcm by multiplying a and b. True or false

A: if GCD(a,b) is 1, We can find lcm by multiplying a and b.   This statement is True.

Q: Is it true that GCD(6,14,119) x LCM(6,143,119)= 6x143x119?

A: We know that GCD(a,b,c) × LCM(a,b,c) = axbxc

Q: Show that a6-1 is divisible by 168 whenever (a, 42)=1.

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Q: For each positive integer n, define an = ((2+√3)" + (2-√3)") 2 It is known that an is a positive…

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Q: Find all x such that 7x+3 is divisible by 9.

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Q: Let Ci=[-2i,2i] for all nonnegative integers i. a. C1 U C2 U C3 b. n^100i=1Ci

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Q: find In(2 i+3)

A: We have to find ln2i+3.

Q: Number 332 – 1 has exactly two divisors greater than 75 and less than 85. What is their product?

A: We need to find two divisors of 332-1 between 75 and 85.  Now, we can use the identity a2-b2=a-ba+b…