show that for all integers x and y (x-y)3=x3-y3(mod3)

Q: Given 6x + 2 ≡ 101 (mod 7), find an integer z such that 2x ≡ z (mod 7)

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Q: Determine the positive real numbers x and y such that • x + y = 4 and 2.n2 + y² is small as…

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Q: greatest common divisor(g.c.d)

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Q: Prove that the K4 is not consecutive.

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Q: Show that if x+yi=(a+bi)- is true, then x-yi=(a-bi)-is all real numbers). true (x, y, a, and b are

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Q: How many triples (x1, 2, 13) of nonnegative integers are there where Xi + x2 + x3< 11. Suggestion.…

A: From the given information. The given inequality is as follows. The suggestion given is to convert…

Q: Verify that v2+ V5 is algebraic over Q.

A: Algebraic number :- An algebraic number is a number that is a root of a non-zero polynomial in one…

Q: x^4 + 2x +12 = 0( mod24) All that is not equivalent to polynomial congruence Find solutions.

A: We must identify values of that fulfill the congruence equation x^ 4 + 2x +12 ≡ 0 (mod 24) in order…

Q: Determine the smallest subring of Q that contains 2/3.

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Q: Find the least residue of  -5 -46 modulo 14.

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Q: Find the number of ordered pairs (m,n) such that m and n are positive integers in the set {1, 2,…

A: Let us consider Tm=2m+1.  m Tm 1 3 2 5 3 9 4 17 5 33 6 65 7 129 8 257

Q: Which of the following linear congruence has 1 incongruent solution? (a) 3x = 9 (mod21) (b) 14x = 12…

A: The solution is given as

Q: The coefficient of x³ in (1 + x² + x² + x6)4 is determined by the 4-tuples o integers (a1, a2, a3,…

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Q: (b) Find 95! (mod 96).

A: We have to find the value of 95!(mod 96). Since 95!=95*94*93*…*8*7*6*5*4*3*2*1.

Q: Find all solutions to the following quadratic congruences by first making the leading coefficient 1…

A: Topic:- algebra

Q: Prove that the roots of X2+(1-K)x+k-3=0 are real for all values of k?

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Q: 6: Prove by contradiction that for any positive integer x, x+ 49 x ≥ 14.

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Q: How would you use the existence and uniqueness theorem here?

A: Here the given initial value problem is,.Existence and Uniqueness theorem :The solution of an…

Q: Show that if x is an integer, then gcd(x + 1, x2 – x + 1) divides 3. -

A: First, we find gcdx+1, x2-x+1 Now, factors of x+1 are x+1, 1 x2-x+1 is a quadratic equation of the…

Q: Find all the values of x such that X 4²x17 * 4 + 16 = 0

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Q: 2. Encrypt the message STOP POLLUTION by translat- ing the letters into numbers, applying the given…

A: let's encrypt the message "STOP POLLUTION" using the given encryption functions one by one.For the…

Q: Let m be a positive integer and suppose that the only prime divisors of m are 2, 3, 5 and 11. Show…

A: Given: Let m be a positive integer and suppose that the only prime divisors of m are 2, 3, 5 and 11.…

Q: 3. Show that all integers n ≥ 2 can be expressed as 2x + 3y for some nonnegative integers r and y.

A: Mathematical induction is a proof technique used in mathematics to establish the truth of a…

Q: 2x² – 3x = 9(mod13) X = (mod13)

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Q: x² + 4x = 10(mod11) (mod11) X=

A: Given that x2+4x≡10 (mod 11)x2+4x+4≡10+4 (mod 11)x2+4x+4≡14 (mod 11)x2+4x)(x+2)2≡14+11 (mod…

Q: Prove that there are integers x and y such that 10x-13y=1

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Q: Prove the following using a direct proof.  If a,b, and c are integers such that b is a multiple of…

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Q: True or False : 4x ≡ 12 (mod 10) ⟹ x ≡ 3 (mod 10)

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Q: x² + x = 13(mod17) X= * (mod17)

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Q: 8. Suppose that họ, h1, h2, . . . is a sequence défihed as follows: ho = 1, h = 2, h2 = 3, h =…

A: I have given the proof in details

Q: What letter replaces the letter K when the function f (p) = (7p + 3) mod 26 is used for encryption?

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Q: x² - 2x = 8(mod19) X= (mod19)

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Q: If a and b are positive integers such that gcd(a,b)=13, then find the sum of all possible distinct…

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Q: Suppose a and b are +ve integers with d=gcd(a,b) prove that gcd(a/g,b/g)=1

A: # The statement should be gcd(a/d, b/d) =1 instead of gcd(a/g, b/g) =1 Given that d=gcda,b let…

Q: S(x + Vx)dx 73 6.

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Q: 16. Find the set of real values of x for which:/3 - 2x/S/x + 4/. N.Find the set of values of x for…

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Q: Find all integer values of x for which 3x = 4 (mod 8).

A: given congruence equation 3x≡4(mod 8)

Q: et a, b, c be non-zero integers. Suppose that x, y are integers such that ax + by = c. Show that for…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.