All perfect squares are divisible by 2. A.) True B.) False, counterexample of 16 C.) False, counterexample of 15 D.) False, counterexample of 25

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Q: 4. Show that if k is a triangular number, then 8k + 1 is a perfect square.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

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Q: Prove that if n is odd, then 2 is not a square in GF(5n).

A: Given n is odd number We have to show that 2 is not a square in GF5n. We know that the field GF5 is…

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Q: R.2. Let S represent the set of positive integers that are perfect squares, and let C represent the…

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A: First find the Eigen Value and Eigen vector

Q: Discrete

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A: To prove 5 is irrational. Use the method of proof by contradiction.

Q: Prove that if n is odd, then 2 is not a square in GF(5n) In other words, prove that there is no…

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Q: Show that the Poly nomial ac -(6² +1) is K[a,b, cI irreducible in Here KiS Pield.

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A: Recall the following fact about divisibility.

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A: Given: Let's take a,b,c are integer powers of 2. Prove that a3+b4 =c5  does not have a solution.

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A: Given that, m and n are even and both perfect squares.

Q: C) Prove that the product of k consecutive positive integers is divisible by k!

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Q: Exercise 5. Prove that given positive integers a and b, there is a positive integer d such that • d…

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Q: 3. Prove that if n is a triangular number, then so are 9n + 1, 25n + 3, and 49n+ 6. Hint: Recall…

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Q: 3. Prove that if n is a triangular number, then so are 9n +1, 25n + 3, and 49n + 6. Hint: Recall…

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