SOLUTION: Consider the following proposition: There are no integers a and b such that b^2 = 4a + 2. (a) Rewrite this statement in an equivalent form using a universal quantifier by comple

Question 494495: Consider the following proposition: There are no integers a and b such that
b^2 = 4a + 2.
(a) Rewrite this statement in an equivalent form using a universal quantifier
by completing the following:
For all integers a and b,....
(b) Prove the statement in Part (a).

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
You could say something like, "For all integers a and b, b^2 is never equal to 4a+2."

For any integer b, b^2 is congruent to either 0 or 1 modulo 4. 4a+2 is always 2 modulo 4. If b^2 and 4a+2 were equivalent mod 4, then they could be equal but they're different mod 4, so they can never be equal.
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