Tag Archives: remainder

Divided by 5

Find the reminder when is divided by ? Source: NCTM Mathematics Teacher, October 2006 Solution is such a large number that it is impractical to use modulo arithmetic to find the remainder. So we are going to find the remainders … Continue reading

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Divisible by 7

How many four digit positive integers divisible by have the property that, when the first and last digits are interchanged, the result is a (not necessarily four-digit) positive integer divisible by ? Source: NCTM Mathematics Teacher, October 2006 Solution Is … Continue reading

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TV Game Show

On a television show, a player receives points for answering an easy question and points for a hard one. What is the largest integer that cannot be a contestant’s total score of the game? Source: NCTM Mathematics Teacher, October 2006 … Continue reading

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Largest of Five Integers

A set contains five integers. When distinct elements of this set are added together, two at a time, the complete list of different possible sums is , and . What is the largest of the five integers in the set? … 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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Pennies on Table

Some pennies are piled on a table. If you put them into piles of size , or , you always end up with penny left over. There is more than penny on the table. What is the fewest number of … Continue reading

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Find All Integers

Find all integers such that is also an integer. Source: NCTM Mathematics Teacher, December 2005 SOLUTION The expression is an integer if is a divisor of . The divisors of are: Eight integers make the expression also an integer. Answer: 8

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Sum of Terms

In the sequence of numbers , each term (starting with the third) is equal to the term preceding it minus the term preceding that one. What is the sum of the first terms of this sequence? Source: NCTM Mathematics Teacher, … Continue reading

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More Remainders

How many positive integers have a remainder when is divided by ? Source: NCTM Mathematics Teacher, November 2006 SOLUTION If divided by has a remainder , there exists a quotient such that and . which implies that the number of … Continue reading

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Remainder

What is the remainder when is divided by ? Source: NCTM Mathematics Teacher, November 2006 SOLUTION If a polynomial is divided by a polynomial , there exists a quotient polynomial and a remainder polynomial such that with . Though tedious … Continue reading

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