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Nx2
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i just started my second semester with geomtry and am having difficulties with these proofs. i am stuck on this one question which asks:
prove that if n is an odd positive integer, then one of the numbers n+5 or n+7 is dividsible by 4.
so this is what i came up with:
let n = 2k+1
f(n)= n+5
= (2k+1)+5
= 2k+6
= 2(k+3)
So we know that 2 is divisible by 2 and now I am guessing i have to prove that (k+3) is divisible by 2 as well. then by using the factor tree thing we can say that since the 2 is divisible by 2 and (k+3) is divisible by 2, f(n) must be divisible by 4, no? but i don't get how to do this... am i doing something wrong?
i did the same exact method with f(n)= n+7 and ended up with f(n)= 2(k+4).
i just don't get all this proving stuff.
Any help would be appreciated, thanks.
- Tu
prove that if n is an odd positive integer, then one of the numbers n+5 or n+7 is dividsible by 4.
so this is what i came up with:
let n = 2k+1
f(n)= n+5
= (2k+1)+5
= 2k+6
= 2(k+3)
So we know that 2 is divisible by 2 and now I am guessing i have to prove that (k+3) is divisible by 2 as well. then by using the factor tree thing we can say that since the 2 is divisible by 2 and (k+3) is divisible by 2, f(n) must be divisible by 4, no? but i don't get how to do this... am i doing something wrong?
i did the same exact method with f(n)= n+7 and ended up with f(n)= 2(k+4).
i just don't get all this proving stuff.
Any help would be appreciated, thanks.
- Tu