- Calculate the orders of 2 (mod 67) and of 2 (mod 73).

Q: 5. 2x 15 (mod 17) 6. 4x 6 (mod 17)

A: According to our guidelines we can do at most three subpart of a question at a time. So please post…

Q: 4. Find all numbers between -50 and 50 which x mod 13 = 3

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Q: Let a and b be integers satisfying a=3(mod 11) and b=8 (mod 11). If c=3a+4b then None of these c=9…

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Q: b=3(mod19)

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Q: Name all integers from -100 to 100 that are congruent to -1 modulo 25!

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Q: Find 8081 mod 11.

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Q: 2x = 4 (mod 8) a. has no solution b. has infinite solutions c. has a unique solution modulo 8 which…

A: Here 2x≡4 (mod 8). Hence 2x=4+8k, for some integer k. Dividing by 2, x=2+4k, for some integer k.…

Q: 2x² – 3x = 9(mod13) X = (mod13)

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Q: (18)280 mod 125 =

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Q: Find a number a such that 70a = 1 mod 17.

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Q: Simplify (15-54)(mod 4). (15-54)(mod 4) =(mod 4)

A: Simplify          (15 - 54)(mod 4)

Q: Solve x2+3x+2 is congruent to 0 (mod 55)

A: 55=5×11 and gcd(5,11)=1, hence they are co-prime.The given system of equation x2+3x+2≡0mod 55 is…

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: State whether True or False: If A and B are integers and A ≡ 3 (mod 3) and B ≡ 2 (mod 6) then A+B ≡…

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Q: List all the * = 10.

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Q: Find all solutions for 10x = 14 mod 1008

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Q: Use the index system modulo 19 to find all solutions of x³ = 11 (mod 19) and 5ª = 4 (mod 19)

A: In the theory of congruence, Fermat's little theorem is very significant. It says that for any prime…

Q: Which of the following is false? a. (x-y+2) = (x-y-11) (mod13) b. (x-y+2) = (x-y-32) (mod 17) c.…

A: Sol:- Check each statement:- a.x-y+2≅x-y-11mod 13Since, 2 mod 13 = -11 , This statement is…

Q: -2345 (mod 6) -39 (mod 3) -371 (mod 8)

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Q: ere they want me to find a div m and a mod m when a = −33, m = 67. How I solved, I divided -33 into…

A: To find a div m and a mod m when a = −33, m = 67. Given information:  a = -33 m = 67

Q: Find the whole number of (3+12) =7 mod 10

A: The given equation (3x+12) ≡7 mod 10. Consider the following congruence equation (3x+12) ≡7 mod 10.…

Q: Q2/let n be a fixed positive integer and a,b be arbitrary integers. Then a = b (modn) iffa and b…

A: We have to prove that Given statement

Q: If you add n whole numbers (even or odd) when is the sum of the numbers odd? Translate into adding…

A: A number is said to be an odd number if it is not divisible by 2 and is of the form 2n±1  where n∈ℕ.…

Q: 4) Find 25725 (mod 31)

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.