Grom -Schmidt process and prove solve with 4 -2 こ A 4 -1 A)

Q: We know that x^2= 2(mod 112) and try to find the solution of x

A: This is a problem of Number Theory.

Q: 2. By using Fermat's Theorem, solve, 21x = 12(mod 17).

A: First, we simplify the equation by reducing the coefficients modulo 17. This is because in modular…

Q: 7. . Prove that if n = 4k +3 (for some integer k), then 8|(n² – 1). Proof: Let n = 4k + 3 (for some…

A: Given: n=4k+3, for some integer k. To prove: 8|n2-1

Q: For each odd prime p< 31, identify all of the squares and non-squares in Fp.

A:

Q: x3-3x2+27 is congruent to 0 (mod 225)

A: Consider the following problem  x3-3x2+27≡0mod 225 Prime factorization of 225 is 32×52 Now,…

Q: Prove that 1 + 3 + 5 +···+ (2n − 1) = n2 for every positive integer n (a) by adding 1 + 3 + 5 +···+…

A:

Q: Use Euclidean algorithm to obtain x and y satisfying the equation of (5 036, 2 601) = 5 036x + 2…

A:

Q: The inductive step of an inductive proof shows that for k > 4, if 2k > 3k, then 2k+1 > 3 (k + 1).…

A: Solution :-

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT How many positive integers n ≤ 1000 are coprime with N=90

A: We know that 90=2×32×5 Numbers less than 1000 which are divisible by 2 =10002=500 Numbers less than…

Q: 4) The graphs of y=x and y=x make it obvious that x >x for all real number x > 1. Use induction (not…

A:

Q: Using mathematical induction, prove (21-1+2-) = 2n-2-n for all integers n ≥ 0. im1 • You must use…

A:

Q: Prove by, Proof by Contradiction.   (a) If n is an integer, then n2+ n3 is an even number.   (b) If…

A:

Q: Find all the solutions to the linear congruences  (b) 128x = 833 mod 1001 (c) 36x = 30 mod 42

A:

Q: Let p and q be odd primes. Prove that (p^2) q is not a perfect number. [Hint: Factor 1 + p + q + pq…

A: Let σp2q=σp2σq Then we have  σp2q=σp2σq=1+p+p21+q=p3-1p-1q2-1q-1≤p3p-1q2q-1

Q: ) Find all primitive roots modulo 7.

A: We have to find all primitive root modulo 7.

Q: 5n+7 Find supremum of A :|n E N 4n+12

A: Given set isℝ A = 5n+74n+12 | n∈ℕ We know that a number u is the supremum of a nonempty subset S of…