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Depdendent Variable

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Equ. #1:

Equ. #2:

Equ. #3:

Equ. #4:

Equ. #5:

Equ. #6:

Equ. #7:

Equ. #8:

Equ. #9:

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Dependent Variable

Number of inequalities to solve:

Ineq. #1:

Ineq. #2:

Ineq. #3:

Ineq. #4:

Ineq. #5:

Ineq. #6:

Ineq. #7:

Ineq. #8:

Ineq. #9:

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Other Miscellaneous Problems

95. Prove that is irrational. In other words, prove that if r is a rational number then r^2 ≠

96. Let m be an integer. Prove that if m^2 is odd, then m is odd.

97. Let x be an integer. Prove that if x^2 is not divisible by 4 then x is odd.

98. Let x and y be integers. Prove that if xy is even then either x is even or y is even.

99. Let x and y be integers. Prove that if xy is odd then both x and y are odd.

100. Let x be an integer. Prove that if 8 does not divide x^2 − 1 then x is even.

101. Let x, y and z be integers. Prove that is x does not divide yz then x does not divide z.

102. Let a and b be integers. Prove that if ab is odd, then both a and b are odd.

103. Let a and b be integers. Prove that if a − b is odd then a + b is odd.

104. Prove that there exist integers m and n so that 2m + 7n = 1.

105. Prove that there do not exist integers m and n so that 2m + 4n = 7.

106. Let a, b, and c be integers. Prove that if a divides b − 1 and a divides c − 1 then a divides bc − 1.

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