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Gtsh

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I'm stuck for part ii). For part i) I put "If the equation a^2x+bx+cx has at least one integer solution, then either a,b or c is even"
I'm not too sure if it's right or not.
 

Masaken

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I'm stuck for part ii). For part i) I put "If the equation a^2x+bx+cx has at least one integer solution, then either a,b or c is even"
I'm not too sure if it's right or not.
I *think* you would start by basically putting in the quadratic formula:
1668766442775.png
then since x is divided by 2a, and x is an integer, the numerator must be even and = 2xa (which proves that at least b, a or c is even). i'm not too sure though
 

cossine

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I'm stuck for part ii). For part i) I put "If the equation a^2x+bx+cx has at least one integer solution, then either a,b or c is even"
I'm not too sure if it's right or not.
Part i) is correct however I would avoid the use of either or. This because wither or can be taken mean exclusive or.
 

hogzillaAnson

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The contrapositive is given by


Let's prove the contrapositive. We know from the quadratic formula that




Thus it must be the case that b is even. That concludes our proof
 

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