How would I prove this statement...   Every odd integer is the sum of an odd integer and two even integers.

2. Prove the statement: The sum of the squares of any two consecutive integers is odd.

In each of the following statements, n represents a positive integer. One of the statements is true and the other two are false. (A) If n! is even, then n is not prime. (B) If n is a square number, then n is not prime. (C) If n is a prime number and n ≥ 10, then n + 2 is prime or n +4 is prime. (a) Write down which two statements are false and in each case give a counter-example to show that it is false. (b) Prove the true statement.

. Prove by contradiction that there are infinitely many non-negative integers.

Consider the following statement. For all positive real numbers r and s, Vr + s # Vr + Vs. Construct a proof by contradiction for the statement by selecting sentences from the following scrambled list and putting them in the correct order. By the zero product property, at least one of vr or Vs equals 0, which implies that r or s equals 0. But this is a contradiction because r and s are positive. Simplifying the equation gives that 0 2rs. Simplifying the equation gives that 0 = 2yrys. Squaring both sides of the equation gives that r + s = r + 2VTVS+ s. By the zero product property, at least one of r or s equals 0. Squaring both sides of the equation gives that r + s =r + 2rs + s. Proof by contradiction: 1. Suppose not. That is, suppose there exists positive real numbers r and s such that Vr + s = Vr + vs. 2. By the zero product property, at least one of v(r) or V(s) equals 0, which implies that r or s equals 0. v Select-- 3. 4. Select--- 5. Select- 6. Thus, we have reached a…

Prove that the difference between two integers is odd if and only if exactly one of the integers is odd.

Prove that 2 - 2 · 7 + 2 · 72 – ... + 2(-7)" = (1 – (-7)n+1)/4 whenever n is a nonnegative integer.

Let x be an integer. Prove or provide a counterexample: If 4x+7 is odd, then x is odd.

Prove that 3, 5, and 7 are the only three consecutive odd integersthat are prime.

Please answer True or False for the following Statements... 1. Let x be an integer. Then if 7x+4 is even, then 3x-11 is odd. 2.Let x and y be real numbers. If x^2-4x = y^2-4y and x!=y then x+y=4 3. There exists no positive integer n such that 2n<n^2<3n