Use Hensel’s Lemma and Chinese Remainder Theorem to find all solutions to x^2 + 3x + 17 ≡0 (mod 300)

Q: (a^2 + 1)(b^2 - 1)=c^2 + 3333 prove that it doesn't have an integer solution

A:

Q: for x belonging to Z,  prove or disprove 2x^2 +x +1 must have a remainder 1, 4, or 5 when divided by…

A: Given statement is false

Q: Solve y² = 37(mod 77)

A: We have to find the value of y  Using quadratic reciprocity property we find value of y

Q: (e) x³ + 4x - 12 = 0 (mod 7³) 3

A: Hensels lemma will be the only result which shall be used in solving this problem. The details are…

Q: How many non-negative integer solutions are there to the equation rị + *2 + x3 = 21

A:

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: What are the 5th roots of -1? Show complete solution

A:

Q: 3 62³³ +52²2²-32-2 (2+1)

A: Since you have posted multiple questions i can do one question and in first question given (x-1)…

Q: Use Euler's Theorem to compute and reduce 4^1226(mod 35).

A: To solve 41226mod 35 using Euler's Theorem.   Euler's theorem states that if gcda,n=1 then, aϕn≡1mod…

Q: Find all solutions for x, up to congruence 7^78 (mod 79)

A:

Q: Use Chinese Remain solve the following for x

A: We apply the Chinese remainder theorem to solve such questions. Given the equation: X2≡43 (mod 221)…

Q: Va 占>0 !! に

A:

Q: Solve 65x ≡ 2(mod243) by inverse method

A: Given, 65x≡2mod 243 Here gcd65,243=1 Now find the inverse of 65 mod 243.…

Q: 4x-3x² +1 (7) x-2

A:

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

A:

Q: Find all integer solutions to 105x+343y=35 Using Magic Box | Elementary Number Theory

A:

Q: Solve 200X (mod 1001) using the modular invVerses.

A: Given: To explain the given statement as follows, To solve by using the modular inverse.

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: Solve the polynomial congruence x^3 - 3x^2 + 27 = 0 (mod 225). Please be detailed! I’m really…

A: Solution are fully explained in below steps Explanation:

Q: find the sum of squares of all roots of the equation 248 17+4²²_2²+x²4-n²+x²-x+1 - H

A:

Q: Given an odd integer a, establish that a^(2) + (a+2)^(2) + (a+4)^(2) +1 is divisiible by 12 using…

A:

Q: What is the degree of the largest irreducible factor of (x^12)-1 over ℚ?   3 4 6 None of the above

A:

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

A:

Q: Let a be an integer such that the remainder of dividing a by 17 is 15. What is the remainder of…

A: We will find out the required value.

Q: Solve 10x = 13 (mod 53)

A:

Q: Use the Euler Theorem to calculate 17^81(mod 55)

A:

Q: find all 4th roots of 1,296   0,  -6

A: