Find the smallest positive integer for which x mod 3 = 2 and a mod 4 = 3 What is the next smallest integer with this property?

Q: b"=1 (mod n) is valid for which of the following pair (b,n) (9.7,1729) (97,1729) (-97,1729)…

A: Answer

Q: Show that 2 is a primitive root modulo 3" for all n > 1.

A: To prove that 2 is a primitive root modulo 3n for all n≥1.

Q: Find 12 ^– 1(mod 17), the inverse of 12 modulo 17

A: Find an inverse of 12 modulo 17 as follows.

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

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Q: Find all values of x (using congruent notation) for 35x ≅ 3 (mod 89)

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Q: Show that every nonzero residue (mod 17) can be written as a power of 3

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Q: Simplify the following expressions by hand and show your work: 23^421 mod 31 57^2024! mod 43…

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Q: Find the least positive integer n that satisfies the congruence 7 ^128 congruent to n (mod13)

A: Given, 7128≡nmod 13 Find the value of n that satisfies the above congruence.

Q: Prove a2 = c² (mod n), assuming that a, c and n are integers with n > 1 and that a = c (mod n)

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

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Q: Find all solutions of the congmonce 12X = 3 (mod 45)

A: The given problem is to find the all solutions for the given congruence equation.Given congruence…

Q: I have a message 2,3,6,5 (mod.7),  I will find a check digit by multiplying the first and third…

A: Here, First number= 2 Second number =3 Third number= 6 Fourth number= 5

Q: What is 2 ^32 mod (5)?

A: mod is the function whose output is always positive. mod is represented by .

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

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Q: What is the inverse of 16 modulo 43 i.e. which number a has the property that 16*a has the remainder…

A: From question we have to find the inverse of 16 modulo 43. i.e  16*a mod(43)=1 It can also be…

Q: Find the inverse of 47 mod 30 or 47 x = 1 (mod 30)

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Q: determine what number the sum is congruent to in mod 3, 6+4 = __ (mod 3)

A: First we add the numbers, then check for the remainder on dividing the result by 3 and that will be…

Q: To Determine the value that 46 is congruent to IN modulo 7

A: Note that, If a and b are integers and n > 0, then a ≡ b (mod n) to mean n|(b − a) and It can be…

Q: 17!=1(mod19). Select one: True False

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Q: Prove that a1 + a2 = b₁ + b₂ mod n.

A: We have to prove that a1+a2=b1+b2 (mod n).Given:a1≡b1 (mod n)a2≡b2 (mod n)This means there exist…

Q: Show that y = x (mod p) leads to -y = -x (mod p).

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Q: there are 3 square roots of 0 when we work mod 45 give all 3 of them

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Q: compute 13 inverse (mod 19) * also known as 13 to the power of -1 * by listing the multiples. Show…

A: Solution:-

Q: List all the * = 10.

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Q: 237 (mod 10)

A: We use the definition of a (mod b) to find the value of 237 (mod 10).

Q: 2x² + 3x = 14(mod19) X = * (mod19)

A: Given,            2x2+3x≡14 (mod 19).