ere exists an integer a with 9p +1 = x³. Let n be an integer. Show that if 2 + 2/1+ 12n² is an integer, then it is the square an integer.

Q: Select two positive integers a and b with 5 <  a  ≤  20  and 5  <  b ≤  20.

A:

Q: Show that the square of any positive Integer is of the form 3m or 3m+1 for some integer m

A:

Q: Show that the square of any integer is of the form 3m or 3m+1 but not of form 3m+2.

A: Proof :-

Q: 1) Show that the square of an odd integer is odd. 2) Show that the product of two odd integers is…

A:

Q: Declare x as an integer From all x from -5 to 2 Print 9x -7

A:

Q: Show that the polynomial 1+x+x² +...+xP-1 . where p is a prime number, is irreducible over the field…

A:

Q: antip . Prove that 4" -3"-7 is a multiple of 84 for each positive even m.

A:

Q: Step by step else downvote, with clear handwriting. Prove that for any real number x, there exits a…

A:

Q: 4 (ii) 16 | at + 15.

A: Step-1 1)16|a4+15

Q: Express the following statement using N-notation.: 12 (3x + 4) for all real numbers x > 2. x + 2

A: Consider the given statement.

Q: at a, b and c be real numbers such that a #0 and ac+bc+c 4ac.

A: Given data is : a , b and c are real number such that a≠0 and ac+bc+c2&lt;0 Show that b2&gt;4ac

Q: Using Fermat’s little theorem to show that 42 | n7 −n, where n is a positive integer.

A:

Q: Given any real numbers a and d, consider the expression (a + md) + (a + (m + 1)d) + (a + (m + 2)d) +…

A:

Q: sing direct proof, prove the following statements: 1. Prove: If x2-4=0, then x = 2 or x = -2. 2. If…

A: follow next step

Q: Disprove the statement: There is a real number x such that xº +x* +1 = 2x².

A:

Q: 1. Prove that the sum of an integer and its square is even

A:

Q: Prove that the sum of the squares of two odd integers cannot be the square of an integer.

A:

Q: O INTENATUNAL SCHUUL Find the condition for 2x² +3kx + 4c to be positive for all real values of .

A: To find the condition for 2x2+3kx+4c  to be positive for all real values of x.

Q: a.Given an integer a, then a² + 4a + 5 is odd if and only if a is even. b. There exists a positive…

A: Since you have posted multiple subpart questions, we will solve the first three questions for you.…

Q: prove the following statement.

A:

Q: - 5. Prove that an integer n is odd if and only if n° – 3 is even.

A: Answer

Q: What is the conjugate to the following binomial?  1+sinx

A:

Q: For positive integers a and b, show that a ab

A: Consider the provided question, For positive integers a and b,  we need to show that, xab=xab

Q: (d) Prôvé that the square of every prime number greater than 3 is one more than a multiple 24.

A:

Q: 10. Which of the following are roots of x3- 3x²– 45x-81? -3 and 9 -4 and 8 -2 and -1 -1 and 9

A: Simplification