Question

find all positive integers n such that n×2^n + 1 is divisible by 3 .​

Answer 1

Answer:

Hint. Note that

n2+1n+1=n2−1+2n+1=n−1+2n+1.

share improve this answer follow

answered

Apr 24 '18 at 16:30

Robert Z

127k●1212 gold badges●8484 silver badges●164164 bronze badges

Up vote

5

Down vote

Hint:

n2+1=(n+1)(n−1)+2

n+1 divides n2+1 if and only if it divides 2

share improve this answer follow

answered

Apr 24 '18 at 16:30

CY Aries

22.2k●11 gold badge●2424 silver badges●5151 bronze badges

Up vote

2

Down vote

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)

mark as brainiest