Question

Show that 12 divide n²+(n+2)²+(n+4)²+1for infinitely many integers n.

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Answer 1

Answer:

Step-by-step explanation:

to prove n^2 + (n+2)^2 + (n+4)^2 + 1 is divisible by 12

simplyfying (opening the bracket)

we get

n^2+n^2+4+4n+n^2+16+8n+1

= 3n^2+12n+21 should be divisible by 12

or it can be shown as

$\frac{3n^2 + 12n + 21}{12}$=

${\frac{3(n^2 + 4n + 7)}{12}}$

we have to prove

n^2+4n+7 is divisible by 4

but if we put value of n as a positive integer , you will find out the resulting integer will be odd meaning it isnt divisible by 4 or therefore you can say that your question is wrong , just check it for n = 4 , it doesnt works

hope it helps pls mark as brainliest