Prove that there is NO perfect square of the form 3n 2Solut

Prove that there is NO perfect square of the form 3n + 2?

Solution

Any integer is of the form 3m, 3m+1 or 3m+2., and their squares are 9m², 9m² +6m+1 , 9m² +12m+4 .

These numbers are of the form 3n, 3n+1 and 3k+1 .(In other words, a square integer is either divisible by 3 or leaves a remainder 1 when divided by 3)

Thus there is no perfect number of he form 3n+2.,