I just started learning gr. 12 discrete math a few days and I’m already having trouble with two very similar questions…(adsbygoogle = window.adsbygoogle || []).push({});

Using deductive proof

1) Prove that if 4 is subtracted from the square of an integer greater than 3, the result is a composite number.

2) Prove that if 25 is subtracted from the square of an odd integer greater than 5, the resulting number is always divisible by 8.

I started 1) by x2-4 = composite number, x > 3 I realized I could factor it down to (x-2)(x+2) = composite number, but I got lost from there.

Then I started 2) in a similar manner by (x2-25)/8. However I’m not sure if the equation is correct so I stopped there.

As you can tell, I’m not exactly the best at deductive proving. So thanks in advance.

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# Number theory (deductive proof)

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