Let n is any positive integer if 3 divides (n-2) then 3 divides (n^2+n)

puntdald8

puntdald8

Answered question

2022-09-10

Let n is any positive integer if 3 divides (n-2) then 3 divides ( n 2 + n )

Answer & Explanation

Zayden Dorsey

Zayden Dorsey

Beginner2022-09-11Added 18 answers

Let m is any positive integer if 3 divides (n-2) then 3 divides n 2 + n
n 2 3 = k n 2 = 3 k n = 3 k + 2
We have prove that 3 divides n 2 + n = k 1 n 2 + n = 3 k 1 m 2 + n = ( 3 k + 2 ) 2 + ( 3 k + 2 ) = 9 k 2 + 12 k + 4 + 3 k + 2 = 9 k 2 + 15 k + 6 = 3 ( 3 k 2 + 5 k + 2 ) m 2 + m = 3 k 1 m 2 + n 3 = k 1
3 divides

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