Tag Archives: consecutive integers

Product of Consecutive Integers

How many integer pairs satisfy the equation ? Source: NCTM Mathematics Teacher, September 2006 Solution We construct products of positive consecutive integers and see which ones if any can be expressed as a power of . is the only such … Continue reading

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Least Positive Integer

What is the least positive integer for which the expression simplifies to an integer? Source: NCTM Mathematics Teacher, October 2006 Solution We look for the smallest sum of positive consecutive integers that is a perfect square  a perfect square Answer: Alternative solution … Continue reading

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Largest Divisor

Select any prime number greater than . Square it and subtract . What is the largest number that must be a divisor of the result? Source: NCTM Mathematics Teacher, January 2006 SOLUTION Suppose is a prime number greater than . … Continue reading

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Sum of Consecutive Numbers (Part 2)

The sum of consecutive positive integers is . Find all possible values of . Source: NCTM Mathematics Teacher, December 2005 SOLUTION Let be the sum of consecutive positive integers with the first term equal . If we add the first … Continue reading

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What Digit?

A digit is placed in each empty square in the grid so that each row and each column contains the digits . What digit is placed in the square at the bottom right corner? Source: NCTM Mathematics Teacher, November 2006 … Continue reading

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2008 As Sum of Consecutive Integers

The number can be written as a sum of consecutive integers such that the number of terms in the sum is twice the number of factors of . Find the smallest of these consecutive integers. Source: NCTM Mathematics Teacher 2008 … Continue reading

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Sum of Four Consecutive Integers

How many positive multiples of that are less than are the sum of four consecutive integers? Source: NCTM Mathematics Teacher SOLUTION The pattern is These multiples of when plotted on a number line are separated by an interval of . … Continue reading

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98 Powers of Two

Find the value of the following expression: Source: mathcontest.olemiss.edu 4/9/2012 SOLUTION We simplify the expression by using the identity We calculate as follows The sum is made up of 3’s and 4’s. How many 3’s are there? The value of … Continue reading

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101st Group

101st Group Group the consecutive counting numbers as follows: (1), (2, 3), (4, 5, 6), (7, 8, 9, 10), . . Notice that there is one number in the first group, two numbers in the second group, three in the … Continue reading

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Consecutive N

The sum of consecutive positive integers is 1998. If is odd, what is the greatest possible value for ? Source: mathcontest.olemiss.edu 9/26/2011 SOLUTION Before tackling this problem we should revisit two formulas related to the sum of consecutive positive integers. Let where … Continue reading

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