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Find the integers. 21. The sum of the squares of two consecutive positive integers is 265. Find the integers. 22. The sum of the squares of two consecutive positive integers is 181. Find the integers. 23. For two consecutive positive odd integers, the product of twice the smaller and the larger is 126. Find the integers. 24.

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May 12, 2014 · Basically, yes. When n is even and more than two, the sum of the consecutive integers is also even, making the sum non-prime if it’s bigger than 2. And if n is odd, the sum of the consecutive integers will be divisible by n, making that sum not prime, unless n is 1 and the single number is 1, since a prime numbers are divisible by 1. About Sum of Positive Integers Calculator . The Sum of Positive Integers Calculator is used to calculate the sum of first n numbers or the sum of consecutive positive integers from n 1 to n 2. Sum of Consecutive Positive Integers Formula. The sum of the first n numbers is equal to: n(n + 1) / 2. The sum of consecutive positive integers from n 1 ...

Introduction to Proofs Rational Numbers Irrational Numbers Even numbers Odd numbers Methods of Proving Theorems Direct Proofs Examples of Solution: To show that this statement is false, we look for a counterexample, which is a particular integer that is not the sum of the squares of two integers.11 Prove that the sum of the squares of any two consecutive integers is always an odd number. (n IS odd (Total for question 11 is 3 marks) 12 Prove that the sum of the squares of two consecutive odd numbers is always 2 more than a multiple of 8 (2/1+1) (In + + CA +9 (Total for question 12 is 2 marks)