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d) there do not exsist integers m abd n such that 12m+15n=1

f) if there exist integers m and n such that 12m+15n=1, then m and n are both positive.

so far for d i have

d) since 12m is always a multiple of 3

and since 15n is always a multiple of 3, then

adding or subtracting two multiples of 3 always yields another multiple of 3, and so

12m + 15n can never equal 1 (it can only equal multiples of 3.)

but I have no idea how to do f. In the back of the book it has a hint that says, "See the statement of part (d). Can you prove that m and n are both negative whenever the antecedent is true?" I don't understand it. Can you please help me?

Thanks for the help!

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# Homework Help: Please help me with this proof!

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