If an integer greater that 4 is a perfect square, then the immediately preceding integer is not prime.

allhvasstH 2020-11-10 Answered
If an integer greater that 4 is a perfect square, then the immediately preceding integer is not prime.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

berggansS
Answered 2020-11-11 Author has 91 answers
Proof:
Consider integer greater than 4, which is a perfect square.
32, 42, 52, 62, 72, 82, 92, 102, 112, s˙ . or
9, 16, 25, 36, 49, 64, 81, 100, 121, s˙
Now we will show that the immediately preceding integer is not a prime.
Hence,
32  1=(3  1) (3 + 1)=2×4×1
42  1=(4  1) (4 + 1)=3×5×1
52  1=(5  1) (5 + 1)=4×6×1

n2  1=(n  1) (n + 1)=(n  1) × (n + 1) × 1
Therefore, we can see that all numbers have two factors which are greater than one.
Further, we know that the prime number is a number that is divisible only by itself and 1. Thus, numbers that have more than two factors are not primes.
Now, we can conclude that, if an integer greater than 4 is a perfect square, then the immediatelly preceding integer is not prime.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more