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Prove that there are 100 consecutive positive integers
Chapter 8, Problem 9E(choose chapter or problem)
QUESTION:
Prove that there are 100 consecutive positive integers that are not perfect squares. Is your proof constructive or non-constructive?
Questions & Answers
QUESTION:
Prove that there are 100 consecutive positive integers that are not perfect squares. Is your proof constructive or non-constructive?
ANSWER:SolutionStep 1Let us assume that first number be m and second number be m+1 then m2 and (m+1)2 be a two consecutive perfect square number.Now, difference between the two consecutive perfect Square number will always be greater than the 100 consecutive integers. (m+1)2 - m2 100