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/sci/ - Science & Math

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1858560 No.1858560 [Reply] [Original]

Can I get a little help please?

>> No.1858574

Induction

>> No.1858585

Induction both ways
1.) base step of 1. plug it in and let it do it's magic.
Assume P(k) where P is that function works, now somehow get P(k+1) through algebraic means
2.) plug in 0
3.)base step of -1. Plug it in and let it do it's magic
Do the same as part 1 except not use P(k-1)

>> No.1858593
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1858593

Try every single possible integer for n. Then you have proven the equation.

>> No.1858602

You basically need to prove that either n, n-1, or n+2 is always divisible by 4.

>> No.1858611

>>1858602
or two of them are divisible by 2.

>> No.1858615

if n isn't divisible by 4, then it is congruent to 1, 2 3 mod 4. If n+2 isn't divisible by 4, then it is congruent to 1 or 3 mod 4. Now we show this implies n^2 -1 is divisible by 4. Consider n^2 -1 mod 4 . If n is congruent to 1 mod 4, then n^2-1 = 0 mod 4, hence it is divisible by 4. If n is congruent to 3 mod 4, then n^2 - 1 = 9-1 = 0 mod 4, hence divisible by 4

>> No.1858619

n(n^2-1)(n+2) = (n-1)n(n+1)(n+2). Since these are 4 consecutive integers, one must be divisible by 4, and hence so must the product.

>> No.1858691

put n equals 1.
get zero as result
zero is divisible by 4
wtfamireading.jpg

>> No.1858723

do it case wise, n is congruent to one of 0,1,2,3. Just plug each of them in and reduce, you always end up showing that the expression is congruent to 0 mod 4.

>> No.1858726

>>1858691
You haven't taken any number theory have you.

>> No.1858730

>>1858691

Yeah... First value I tried to test, no idea what else to do besides test roots

>> No.1858765

>>1858619
Has the simplest correct solution

>> No.1858803

if n is even, then n and n+2 have factors of two, so combined they have a factor of 4.
then you just need to show that n^2-1 is divisible by 4 for every odd number.
1 is easy.
3=9=8
5=25=24
so in general: (n-1)^2+2n-2
or (n-1)^2+2*(n-1)
and n-1 is even
so you have two terms which are both divisible by 4, so the sum is also divisible by 4
QED