Unformatted text preview: n . (Hint: For consecutive integers m and m + 1, what does the theorem say about the possible forms of m (and hence m + 1)?) 8. Prove that if m â‰¡ n ( modd ) and n â‰¡ p ( modd ) then m â‰¡ p ( modd ). 9. Prove the following statement: for all integers n,d with d 6 = 0 d | n iï¬€ n = b n/d c Â· d 10. Prove the following statement by contradiction: There is no least rational number. 11. Prove the following statement by contraposition If the average of two numbers is greater than or equal to one of the numbers. 12. Prove that 3 âˆš 2 is irrational. (Hint: Problem 6 might be useful.)...
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- Fall '08
- Computer Science, Penn State University, consecutive positive integers, consecutive integers