Use a proof by cases to show that 10 is not the square of a positive integer. [Hint: Consider two cases: (i) 1 ¡Ü x ¡Ü 3, (ii) x ¡Ý 4.]
Prove or disprove that if a and b are rational numbers, then ab is also rational. Problem 3
Prove that given a real number x there exist unique numbers n and ¦Å such that x = n + ¦Å, n is an integer and 0 ¡Ü ¦Å < 1.
Prove that there are no solutions in integers x and y to the equation 2x2 +5y2 = 14. Problem 5
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Prove that there are infinitely many solutions in positive integers x, y, and z to the equation x2 + y2 = z2.
Prove that ¡Ì3 2 is irrational.
1/1 CSI2101/UOttawa/MdH/W22
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