Question

Find all integers n > l such that 1" + 2 +...+(n − 1)" is divisible by n.​

Answer 1

Step-by-step explanation:

n2+1n+1 is a natural number

⇔n2+2n+1−2nn+1 is a natural number

⇔(n+1)2−2nn+1 is a natural number

⇔n+1−2n+2−2n+1 is a natural number

⇔n+1−2−2n+1 is a natural number

⇔(n+1)|2

⇔n=1 because n must be a positive odd number and 2 is divisible by (n+1).